ANSWER
[tex]\begin{gathered} <1=39\degree \\ <3=51\degree \end{gathered}[/tex]
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:
[tex]<2=90\degree[/tex]
Since the longer diagonal of the kite bisects the angle [tex]<1=39\degree[/tex]We can solve for <3 using the sum of angles in a triangle:
[tex]<3+39+90=180[/tex]
Simplify and solve for <3:
[tex]\begin{gathered} <3=180-90-39 \\ <3=51\degree \end{gathered}[/tex]
That is the answer.
