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In mathematics, a kite is a special type of quadrilateral. Two pairs of sides are congruent, but opposite sides are not congruent. Exactly one pair of opposite angles are congruent. In kite ABCD shown, the measure of A is twice the measure of C, and B has a measure of 114°. Find the measure of A, C, and D.

Short Answer

Expert verified

A=88,C=44,D=114°

Step by step solution

01

Step 1. Given Information.

The figure is shown below.

02

Step 2. Formula used.

Angle sum property of quadrilateral:

1+2+3+4=360°

03

Step 3. Calculation.

The sides AB and AD are congruent, and BC and DC are congruent. Therefore, the angles between them are congruent, too. Hence,

B=D

Therefore,

D=114°

Let, the C be “x”.

Since, Ais twiceC,

A=2x

Substituting the values of all the angles in the equation of angle sum property of quadrilateral,

2x+114+x+114=3603x+228=360

Shifting the right-hand side and left-hand side values,

3x=3602283x=132

Cross-multiplying the values,

x=1323x=44

Hence,

C=44°A=2xA=2×44A=88°

Therefore, A=88,C=44,D=114°.

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