Question

Find the measure of each missing angle in the following kite.

Answer 1

The measures of the missing angles in the kite are given as follows:

• Angle A: 116.5º.

• Angle B: 109º.

• Angle C: 69.5º.

How to obtain the angle measures?

The sum of the internal angle measures of a polygon of n sides is given by the equation presented as follows:

S = (n - 2) x 180º.

The kite, as shown by the image at the end of the answer, has 4 sides, hence the sum of the measures is given as follows:

S = (4 - 2) x 180º

S = 2 x 180º

S = 360º.

Angles B and D are on the opposite side of the kite, as shown by the image at the end of the answer, hence they are congruent and:

B = 109º.

Adding the measures, the value of x is obtained as follows:

5x + 14 + 109 + 3x + 8 + 109 = 360

8x = 164

x = 20.5.

Hence the measures are given as follows:

• Angle A: 5(20.5) + 14 = 116.5º.

• Angle C: 3(20.5) + 8 = 69.5º.

Missing Information

The model of the kite, with different angle measures, is given by the image at the end of the answer.

More can be learned about the internal angles of a polygon at brainly.com/question/224658

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