Find m∠1 and m∠3 in the kite. The diagram is not drawn to scale.

Solution:

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°.

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Find m∠1 and m∠3 in the kite. The diagram is not drawn to scale.

Summary:

In the kite m∠1 = 39° and m∠2 = 51°.