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Chapter 2: Q10. (page 62)

Describe your plan for proving the following. You don’t need to give all the details.

Given: m∠1=m∠4

Prove: m∠2=m∠3

Short Answer

Expert verified

Angle 2 and angle 3 are equal, that is,m∠2=m∠3.

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Definition of supplementary angles.

The supplementary angles are the angles whose sum is 180°.

03

Step 3. Write the proof of the statement m∠2=m∠3.

From the given diagram it can be noticed that angles ∠1 and ∠2 lie on the straight line.

Therefore, the sum of angles ∠1 and ∠2 is 180°.

That implies, m∠1+m∠2=180°1.

From the given diagram it can be noticed that the angles∠3 and∠4lie on the straight line.

Therefore, the sum of the angles∠3 and∠4 is180°.

That implies, m∠3+m∠4=180°2.

Subtract the equation (2) from (1).

m∠1+m∠2−m∠3+m∠4=180°−180°m∠1+m∠2−m∠3−m∠4=0m∠1+m∠2−m∠3−m∠1=0m∠2−m∠3=0m∠2=m∠3

Therefore, m∠2=m∠3.

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