Question

Triangle XYZ is equilateral with vertices located on circle W. Circle W is shown. Line segments W Y, W Z, and W X are radii. Lines are drawn to connect the points on the circle to form a triangle. Sides Z X, X Y, and Z Y are congruent. Which measurements are correct? Select two options. mArc X Y = 60° mArc Y Z = 120° mArc Z X = 180° m∠XWZ = 60° m∠YWZ = 120°

Answer 1

B. m(arc YZ) = 120°

E. m∠YWZ = 120°

Explanation:

got it right on edge 2023

Answer 2

`arc\ YZ=120^o`

`m\angle YWZ=120^o`

Explanation:

The complete question in the attached figure

we know that

An equilateral triangle has three equal sides and three equal interior angles (the measure of each interior angle is 60 degrees)

`m\angle XYZ=m\angle YZX=m\angle ZXY=60^o`

Remember that

The inscribed angle is half that of the arc it comprises

so

`arc\ XY=arc\ YZ=arc\ ZX=2(60^o)=120^o`

Remember that

Central angle is the angle that has its vertex in the center of the circumference and the sides are radii of it

so

`m\angle YWZ=arc\ YZ=120^o` ----> by central angle