Question

In kite WXYZ, measure of angle XWY=38° and measure of angle ZYW=15°

what is the measure of angle WXY?

enter your answer in the box.

Answer 1

Answer: m<WXY = 127

Answer 2

m∠WXY=127°

Explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle XYW

we know that

The diagonal of symmetry divides the kite into two congruent triangles and it also bisects the pair of opposite angles.

The diagonal of symmetry is the segment WY (see the attached figure)

so

m∠XYW=m∠ZYW

we have

m∠ZYW=15°

so

m∠XYW=15°

step 2

Find the measure of angle WXY

Remember that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

In the triangle XYW

m∠XYW+m∠XWY+m∠WXY=180°

we have

m∠XYW=15°

m∠XWY=38°

substitute the values

15°+38°+m∠WXY=180°

53°+m∠WXY=180°

m∠WXY=180°-53°

m∠WXY=127°