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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.

Respuesta :

calculista

Answer:

Part 1) [tex]m\angle 1=39^o[/tex]

Part 2) [tex]m\angle 3=51^o[/tex]

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

[tex]m\angle 1=39^o[/tex]

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

[tex]39^o+m\angle 3=90^o[/tex] ----> by complementary angles in a right triangle

[tex]m\angle 3=90^o-39^o=51^o[/tex]

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