Question

Geometry Help please!!!

In kite WXYZ , m∠XWY=38° and m∠ZYW=15° .

What is m∠WXY ?

Answer 1

m∠XWY=
`127\°`

Explanation:

we know that

In the kite WXYZ

WX=WZ

XY=ZY

m∠WXY=m∠WZY

m∠XWY=m∠ZWY

m∠ZYW=m∠XYW

so

In the triangle WXY

The sum of the internal angles must be equal to
`180\°`

so

m∠XWY+m∠WXY+m∠XYW=
`180\°`

we have

m∠XWY=
`38\°`

m∠XYW=m∠ZYW=
`15\°`

substitute and solve for m∠XWY

m∠XWY=
`180\°-(38\°+15\°)`

m∠XWY=
`127\°`

Answer 2

Angle WXY = 127 degrees

The diagonals of a kite are perpendicular so the middle angles are all 90 degrees. The angles at W and Y are bisected by the diagonals so both the angles at W are 38 and both at Y are 15. Using the fact that the sum of the measures of a triangle are 180, you can get the other angles of 52 and 75.