Question

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

Given: $m\angle 1=m\angle 4$

Prove: $m\angle 2=m\angle 3$

Short answer

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

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Definition of supplementary angles.

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

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, $m\angle 1+m\angle 2=180°\left(1\right)$.

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, $m\angle 3+m\angle 4=180°\left(2\right)$.

Subtract the equation (2) from (1).

$$\begin{gathered} m\angle 1+m\angle 2-\left(m\angle 3+m\angle 4\right)=180°-180° \\ m\angle 1+m\angle 2-m\angle 3-m\angle 4=0 \\ m\angle 1+m\angle 2-m\angle 3-m\angle 1=0 \\ m\angle 2-m\angle 3=0 \\ m\angle 2=m\angle 3 \end{gathered}$$

Therefore, $m\angle 2=m\angle 3$.