Question

Refer to rectangle ABCD shown below. If m A is 60 degrees and if m 2 is 60 degrees. Find m 1, m 3.

Answer 1

We have a rectangle and we must find m(∠1) and m(∠3).

1. We must use that the interior angles of a rectanhgle measure 90°, then

$\begin{gathered} 60^{\circ}+m(\angle1)=90^{\circ} \\ \\ \end{gathered}$

Then, we must solve the equation for m(∠1)

$\begin{gathered} m(\angle1)=90^{\circ}-60^{\circ} \\ m(\angle1)=30^{\circ} \end{gathered}$

2. We must use that ∠1 and ∠3 are alternate interior angles, so they measure the same

$\begin{gathered} m(\angle1)=m(\angle3) \\ \text{ Knowing that }m(\angle1)=30^{\circ} \\ m(\angle3)=30^{\circ} \end{gathered}$

ANSWER:

m(∠1) = 30°

m(∠3) = 30°