Question

On the kite, vertex A at the top, vertex B at the right, vertex C at the bottom, and vertex D at the left. Side A B is marked congruent to side A D. Side D C is marked congruent to side B C. Diagonal A C and B D are drawn.
Angle D A C is 39 degrees. Find m ∠ 1 and m ∠ 3 in the kite. The diagram is not drawn to scale.

Answer 1

Answer:

Part 1) $m\angle 1=39^o$

Part 2) $m\angle 3=51^o$

Step-by-step explanation:

The picture of the question in the attached figure

Part 1) Find the measure of angle 1

we know that

The longer diagonal of a kite bisects the kite into two equal parts

That means

$m\angle 1=39^o$

In this problem the longer diagonal is the segment AC

Part 2) Find the measure of angle 3

we know that

The intersection of the diagonals of a kite form 90 degrees.

That means ----> The triangle ADO (O is the intersection point both diagonals) is a right triangle

so

$39^o+m\angle 3=90^o$ ----> by complementary angles in a right triangle

$m\angle 3=90^o-39^o=51^o$