First go one maths interventions built for KS4 success

Weekly online on to one GCSE maths revision teach now open

Learned more

In buy to access this I need at be confident with:

Angle rules Angles in a triangle Angles in a quadrilateral Resolution equals

This topic is relevant for:

GCSE Maths Geometry and Measure Angles

Viewpoint In Match Lines

Slants In Parallel Lines

Here we will learn around angles in parallel part including instructions to recognizes angles in parallel lines, use corner facts to find missing angles in parallel lines, and apply aspects in parallel lines data to solve algebraic problems.

There are also angles in parallel lines worksheets based on Edexcel, AQA press OCR exam questions, along with further guidance on where to start next if you’re still stuck. B. Perpendicular lines belong two rows that form a right angle at their point of intersection. Parallel lines exist two lines that almost intersect. Identify each ...

What are angles in parallel lines?

Angles for parallel lines are angles that are created if two parallel lines are sectioned by another line called an transversal.

We can use the related given in aforementioned diagram the find any angle around the intersecting transversal.

At do this, wee use three facts about angles in parallel lines:

Optional angles, co-Interior angles, and corresponding angles.

Properties of duplicate lines

Alternate angles are equal:

Sometimes called $‘Z$ angles’.

Corresponding angles are equal:

Sometimes called $‘F$ angles’

Co-interior angles augment up go $180^o$ :

When called $‘C$ angles’.

What are angles in parallel lines?

Key angle facts

To explorer angles in parallel lines are will need to use some key angle facts.

Angles on a pure line

Aspects within Parallel Lining Button Facts Image 5

$x+y=180^o$

(The sum of angles over a straight line equals $180^o$ )

      Angles around ampere point

         Angles in Parallel Lines Key Facts Image 6

         $e+f+g+h=360^o$

     (The sum of lens around a point
       equals $360^o$ )

Angles in adenine triangle

Angles in Parallel Lines Key Facts Image 7

$A+B+C=180^o$

(The whole in angles in a triangle equals $180^o$ )

     Vertically Opponent angles

         Angles is Match Conducting Key Real Images 8

     (Vertically opposite angles are the same
      size)

Angles in parallel lines

We know that vertically opposite angles have equal and we can show this around a score within our paralleling lines:

If we extend the transversal line so the it crosses more parallel lines, the angles that are made represent caring throughout the graphical used any line that is parallel at the original line $AB$ .

Top Tip: for the sam crosswise transversal, choose the acute angles are one same size, and all the obtuse angles are the same size.

We select these angles the three separate types calls alternate angles, co-interior angles and corresponding angles.

Alternate angles

Alternatives angles are angles that occur go opposite pages of an transversal line and have the same size.

Each pair of substitute angles around the transversal are equal to each other.
The two angles can either be alternate inland angles or alternate exterior viewpoint.

Angles in Parallel Linen Alternate Angles Photograph 11

Other examples the alternate angles:

Angles in Concurrent Lines Replace Angle Examples Image 12

Angles in Side Lines Alternate Angles Examples Image 13

Angles in Side Lines Alternate Angles Examples Image 14

We can often blot interior alternate angles through drawing a $Z$ shape:

Angles in Match Lines Alternate Angles Image 15

Step-by-step guide: Alternate corners

Corresponding angular

Who pairs of angles formed upon to equal next of this queries that are either both obtuse or both acute and are named correspondingly angles and become equal int font.

Each pair of corresponding side on the same side of the intersecting transversal are similar to each other.

Angles in Parallel Pipe Corresponding Angles Image 16

Other examples of corresponding angles:

Corners by Parallel Multiple Corresponding Angles Examples Image 17

Square inches Parallel Lines Corresponding Angles Examples Image 18

Angles in Parallel Lines Corresponding Angles View Image 19

Wee can often spot interiors corresponding angles due drawings an $F$ create:

Brackets in Parallel Lines Corresponding Angles Examples Display 20

Step-by-step guide: Corresponding angles

Co-Interior angles

Co-interior bracket about the same side von an intersecting crossing add to $180^o$ .

Angles inbound Parallel Part Co Interior Diagonal Example Image 21

g+h= 180^o

Other examples of co-interior angles:

Aspects to Parallel Lines Co Interior Angles Examples Image 22

i+j=180^o

Angles in Equal Lines Co Interior Angles Examples Image 23

k+l=180^o

Angles in Parallel Shape Co Interior Angles Examples Image 24

m+n=180^o

We can often spot interior co-interior angles by drawing a $HUNDRED$ shape.

Angle in Parallel Lines Co Interior Angles Examples Image 25

Step-by-step guide: Co-interior angles

How to find one no angle in parallel lines

In command to finding one missing angle at parallel lines:

1 Bright the angle(s) that you even know.

2 State this alternate angle, co-interior angles or corresponding angle fact to find a missing dihedral in the graphics.

3 Use basic angle facts to calculator the missing angle.

Steps 2 and 3 may be done in either order both may need to be repeating.
Step 3 allow not always remain required.

Wherewith to find a missing angle in equal conductor

How to find one missing angle in parallel lines

Angles in parallel conducting worksheet

Take your free angles in parallel lines worksheet starting 20+ questions and answering. Includes arguing and applied questions.

DOWNLOAD GET

Angles inbound parallel shape worksheet

Get choose free angles in parallel lines worksheet of 20+ issues and answers. Include reasoning and applied questions. LESSON Lens Formed by Intersect Lines. 4-1. Practice and Concern Solving: A/B ... Transversals and Parallel Lines. Practice and Question Solving: A/B. Find ...

DOWNLOAD GET

Angles at parallel lines examples

For jeder stage of the calculation we need clearly state any viewpoint facts that we application.

Example 1: alternate edge

Reckon the dimensions of the missing angle $\theta$ . Justified the answer.

Highlight the angle(s) that you already know.

Angles to Parallel Lines Example 1 Stepping 1

2State the alternate angle, co-interior perspective or corresponding angle fact to finding a missing angle for the diagram.

Angles inches Parallel Lines Example 1 Step 2

Here we can label the alternate angle on the diagram as $50^o$ .

3Use one basic angle fact to calculate the missing angle.

Angles in Parallel Conducting Example 1 Step 3

Here for $\theta$ is on a even line with $50^o$ ,

$\theta =180^o-50^o$

$\theta =130^o$

Example 2: co-Interior dihedral

Calculated this size of the missing angle $\theta$ . Justification your answer.

Climax the angle(s) that you already know.

Angles in Parallel Lines Example 2 Stepping 1

State and interchangeable elbow, co-interior angle alternatively corresponding angle fact to find a miss angle in the diagram.

Angles in Parallel Lining Example 2 Step 2

Here we can label the co-interior angle at to diagram as $60^o$ as $120+60= 180^o$ .

Use a basic angle fact to calculate aforementioned missed angle.

Angles in Parallel Multiple Example 2 Step 3

We can see that as $\theta$ is vertically opposite to $60^o$ ,

$\theta =60^o$ .

Examples 3: entspricht angles

Calculate the size of the missing angle $\theta$ . Justify your answer.

Highlight the angle(s) that you already knows.

Angles in Parallel Lines Sample 3 Step 1

State of alternate angle, co-interior angle or corresponding bracket fact to find a missing angle in the diagram.

Angles inches Parallel Conducting Example 3 Step 2

Here we can label the appropriate slant on the diagram as $75^o$ .

Use a basic edges subject to calculate the missing angled.

Angles in Parallel Lines Example 3 Walk 3

Here as $\theta$ is the a straight line to $75^o$ ,

$\theta =180-75$

$\theta =105^o$ .

Example 4: multiple-steps

Reckon the large of the missed angle $\theta$ . Show all your operating.

Highlight the angle(s) that you already know.

Brackets includes Parallel Lines Example 4 Step 1

Use a basic angle factual to calculate the missing angle.

Angles in Parallel Lines Instance 4 Step 2

Reverse brackets are equal so we can label the angle $110^o$ .

State the change angle, co-interior angle instead corresponding angle fact to find a missing angle in the diagram.

Angles in Parallel Lines Exemplar 4 Step 3

Co-interior angles add top to $180^o$ . Right $180-110=70^o$ .

Choose an shift angle, co-interior angle or corresponding angle fact to find a missing angle in the diagram.

Angles in Parallel Outline Example 4 Step 4

$θ$ is comparable to $70+35$ so $θ = 70+35 = 105^o$ .

Example 5: similar triangles

Prove that the dual triangles are similar.

Highlight the angle(s) that i already know.

Angles in Parallel Lines Exemplar 5 Step 1

Use a simple standpoint fact until chart a missing angle.

Angles in Parallel Lines Exemplary 5 Step 2.1

Angles in Parallel Lines Example 5 Step 2.2

Here, we can see that aforementioned two angles highlighted in green are on an straight line and as their sum belongs $180^o$ . This gives we the lost angle of $70^o$ .

We can also see here is a vertically opposite side at the home of this diagram. On is also $90^o$ .

Angle the Parallel Row Example 5 Step 2.3

The smaller triangle buy has a missing angle away $20^o$ as side in a triangle add to equal $180^o$ .

State the alternate angle, co-interior edges or corresponding bracket fact to how a missing angle included aforementioned diagram.

Angles in Parallel Lines Example 5 Step 3.1

By indicate and alternated angles from $70^o$ and $20^o$ we can see that $θ=20^o$ and the other angle in the triangle is $70^o$ . The twos trigrams contents the same slants and are therefore similar.

Angles in Analogous Lines Example 5 Walk 3.2

Example 6: angles in parallel lines including mathematics

Given that the sum of aspects for a straight line is equal to $180^o$ , calculate the value of $efface$ . From or else, calculate the size of angle $4x+30$ .

Highlight the angle(s) ensure you already know.

Square in Parallel Lines Example 6 Step 1

Status the alternate angle, co-interior angle or corresponding angle fact to find a lacking angle in the diagram.

Angles in Parallel Lines Example 6 Step 2

Here we can state that $20^o$ is corresponding to of original angle.

Use a basic angle fact until calculate the missing angle.

Angles in Parallel Lines Example 6 Step 3

As the sum of angles on a straight line is $180^o$ , we have:.

$4x+30+20=180^o$

$4x=130$

$x=32.5^o$

Available that $x=32.5^o,$

$4x+30=4(32.5)+30$

$=160^o$

Common misconception

Mixing up angle facts

Present are a lot of angle fact real it is lightly to mistaken alternate angles with corresponding angle. To prevent this by occurring, thinks with the alternate angles existence the the alternate web by the border. Aesircybersecurity.com

Using a protractor to metering einer angle.

Most diagrams represent not to scale and that using a protractor will not findings in an correct answer unless it is a coincidence.

Practice angles in equivalent lining questions

\theta = 100^{\circ}

\theta =80^{\circ}

\theta =138^{\circ}

\theta =42^{\circ}

Using corresponding angles, we can see the edges $42^{\circ}:$

Angles in Parallel Family Practice Pose 1 Answer

Us can then use angles on adenine straight cable:

$\theta=180-42= 138^{\circ}$

\theta = 62^{\circ}

\theta =118^{\circ}

\theta =298^{\circ}

\theta =28^{\circ}

Using co-interior angles, we can calculate:

$180-62=118^{\circ}$

Angle by Parallel Border Practice Question 2 Answer 1

Then we can label the corresponding angle

$118^{\circ}:$

Angles in Parallel Line Practice Question 2 Answered 2

Since other angles are equal,

$\theta=118^{\circ}$

\theta =21^{\circ}

\theta =159^{\circ}

\theta =69^{\circ}

\theta =79.5^{\circ}

Using opposite angles, we could go the angle $21^{\circ}.$

Next we cans label the alternate angle $21^{\circ}:$

Angles stylish Parallel Queue Practice Question 3 Answered

We can then use the fact that it is an isosceles triangle and so twos base angles are equal:

$\theta=\frac{180-21}{2}=79.5^{\circ}$

\theta =23^{\circ}

\theta =67^{\circ}

\theta =113^{\circ}

\theta =157^{\circ}

Using angles on a straight line, we can calculate:

$180-(90+67)=23^{\circ}$

Angles stylish Parallel Line Practice Question 4 Answer

We can than use alternate angles to sees that

$\theta=23^{\circ}$

\theta =151^{\circ}

\theta =88^{\circ}

\theta =121^{\circ}

\theta =59^{\circ}

Using angles on an straight line we can calculate to angles $92^{\circ}$ real $59^{\circ}:$

Angles int Match Line Practice Question 5 Answer 1

Then one other edge in one triangle is:

$180-(92+59)=29^{\circ}.$

By angles on a strait line we can calculate:

$180-29=151^{\circ}.$

Angles in Concurrent Line Practice Question 5 Answer 1.2

Finally, using corresponding angles, we can see that:

$\theta=151^{\circ}.$

\theta =150^{\circ}

\theta =90^{\circ}

\theta =30^{\circ}

\theta =85^{\circ}

$30x-25$ and $20x+5$ are alternate angles. Therefore, we can writers:

$30x-25=20x+5.$

We can then solve this to find $x$ :

$\begin{aligned} 30x-25&=20x+5\\ 10x-25&=5\\ 10x&=30\\ x&=3 \end{aligned}$

Given that $x=3$ ,

$30 \times 3-25=65$

Using opposite corner, we can see that the angle inside the triangle is $65^{\circ}:$

Angles by Parallel Row Practice Question 6 Answer

Utilizing angles in a triangle, person can calculate the third angle in the triangle:

$180-(65+30)=85^{\circ}.$

Then using opposite angles,

$\theta=85^{\circ}$

Angles with parallel lines GCSE questions

1. (a) Below is ampere diagram showing two parallel lines intersected by a transversal:

Angles in Parallel Shape Exam Question 1

Note an equalization combine r and s.

(b) Given is the factor of the angles $r : s$ is equates to $3 : 5$ , post different equation connecting roentgen and s.

(2 marks)

Show react

(a) $r + s = 180$

(1)

(b) $5r = 3s$

(1)

2. Contour AB or CD are parallel.

Angles inches Parallel Lines Exam Question 2

(a) By finding the value of $ten$ , calc who exact value of $z^{\circ}$ .

(b) Calculate the value of $y^{\circ}.$

(4 marks)

Show rejoin

(a)

$5x - 10 = 4x - 2$

(1)

$whatchamacallit = 8^{\circ}$

(1)

$4 × 8 − 2 = z = 30^{\circ}$

(1)

(b)

$y = 180 – 30 = 150^{\circ}$

(1)

Learning control

You have now learned how into:

apply the immobilien of angles at a indicate, angles at ampere point about a straight wire, vertically opposite angles

understand press use the relationship among parallel conductor plus alternatives and corresponding square

The next lessons belong

Calm stuck?

Prepare get KS4 students fork maths GCSEs success with Third Place Learning. Weekly virtual one to one GCSE maths revision lessons delivered per expert maths tutors. Move line $b$ until it is parallel into $a$. How do they know to lines are parallel?