In the kite, angle 1 is 39°, and angle 2 is 51°. Diagonals AC and BD intersect at right angles, confirming these angle measures.
Given figure is a kite.
The diagram is not drawn to scale.
We have to find the measure of angle 1 and 3 in the kite.
From the figure,
Kites have two sets of equivalent adjacent sides and one set up of congruent opposite angles.
So, sides AB and AD are equivalent adjacent sides.
m∠1 = 39°
AC and BD are diagonals.
Diagonals of a kite always meet at right angles.
Let the diagonals intersect at point O.
From right triangle AOB,
m∠1 + m∠2 + m∠O = 180°
39° + m∠2 + 90° = 180°
m∠2 = 180° - 90° - 39°
m∠2 = 90° - 39°
m∠2 = 51°
Therefore, m∠1 = 39° and m∠2 = 51°.