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Chapter 4: Q10. (page 165)

Find the measure of each numbered angle.

Short Answer

Expert verified

The angles are:

m∠1=75∘m∠2=40∘m∠3=40∘m∠4=65∘

Step by step solution

01

- Consider the diagram. 

Here, AB∥CD.

02

- Show the calculation.

Since, AB∥CD,

Here, m∠4=m∠C=65°, since they are corresponding angles, where AC is the transversal and AB is parallel to CD.

m∠3+m∠AED=180° …… [linear angles]

That implies,

m∠3+140°=180°

Subtract 140° from each side, then,

m∠3=180∘−140∘m∠3=40∘

Now, m∠2=m∠3=40°, since they are alternate interior angles, where AE is the transversal and AB is parallel to CD.

m∠1+m∠3+m∠C=180∘m∠1+40∘+65∘=180∘m∠1+105∘=180∘

Subtract 105° from each side, then,

m∠1=180∘−105∘m∠1=75∘

03

- State the conclusion.

Therefore,

m∠1=75∘m∠2=40∘m∠3=40∘m∠4=65∘

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