Question

WXYZ is a kite. If the measure of angle WXY is 120°, the measure of angle WZY is 4x° and the measure of angle ZWX is 10x°, find the measure of angle ZYX.

Answer 1

100

Explanation:

Angle ZWX and angle ZYX are congruent.

360 = 120 + 4x + 10x + 10x

360 = 120 + 24x

240 = 24x

10 = x

The measure of angle ZYX is equal to 10(10) = 100°

Answer 2

100 degrees

Explanation:

Remark

The endpoints of the smaller diagonal of a kite, intersect the vertexes of 2 equal angles. Put in simpler language, if x is at the top of the kite and x is the vertex of the larger angle between the top and bottom angles, then the other two angles (left and right) are equal.

In still simpler language. <W = <Y

Equation

<X + <W + <Z + <Y = 360 All quadrilaterals have 360 degrees for their interior angles.

Givens

• <X = 120
• <W = 10x
• <Z = 4x
• <Y = 10x

Solution

• 120 + 10x + 10x + 4x = 360 Gather like terms on the left
• 120 + 24x = 360 Subtract 120 from both sides
• 120- 120 + 24x = 360 - 120 consolidate
• 24x = 240
• x = 10

Answer

• Since <ZYX = 10x
• <ZYX = 10*10 = 100 degrees.