Question

Find m∠1 and m∠3 in the kite. The diagram is not drawn to scale. (image attached)thank you ! :)

Answer 1

ANSWER

$\begin{gathered} <1=39\degree \\ <3=51\degree \end{gathered}$

EXPLANATION

We want to find the measures of <1 and <3 in the kite given.

The diagonals of a kite bisect each other at right angles.

This implies that:

$<2=90\degree$

Since the longer diagonal of the kite bisects the angle $<1=39\degree$We can solve for <3 using the sum of angles in a triangle:

$<3+39+90=180$

Simplify and solve for <3:

$\begin{gathered} <3=180-90-39 \\ <3=51\degree \end{gathered}$

That is the answer.