Question

What is the measure of XYZ​

Answer 1

B. 240°

Explanation:

By inscribed angle theorem:

`m\widehat({ZX) } = 2* \angle XYZ\\</p><p>m\widehat{(ZX) } = 2* 60\degree \\</p><p>\purple {\bold {m\widehat{(ZX) } = 120\degree}} \\</p><p>\because m\widehat{(XYZ)} = 360\degree - m\widehat{(ZX)} \\</p><p>\therefore m\widehat{(XYZ)} = 360\degree - 120\degree \\</p><p>\huge \orange {\boxed {\therefore m\widehat{(XYZ)} = 240\degree}} \\`

Answer 2

B

Explanation:

The arc XZ is twice the measure of the inscribed angle XYZ , that is

arc XZ = 2 × 60° = 120°

The complete circumference = 360° , thus

arc XYZ = 360° - arc XZ = 360° - 120° = 240° → B