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°