In the diagram of circle P, m XYZ is 72°. What is the value of x?

Solution:

In the figure, the tangent tangent angle XYZ is

∠XYZ = 0.5(arc ZX - arc XZ)

Substituting the values

72 = 0.5(360 - x - x)

By further calculation

72 = 0.5(360 - 2x)

72 = 180 - x

Let us add x on both sides

72 + x = 180

By subtracting 72 from both sides

x = 108

Therefore, the value of x is 108°.

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In the diagram of circle P, m XYZ is 72°. What is the value of x?

Summary:

In the diagram of circle P, m XYZ is 72°. The value of x is 108°.