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

Based on the inscribed angle theorem, the measurements that are correct are: B. m(arc YZ) = 120°; E. m∠YWZ = 120°.

What is the Inscribed Angle Theorem?

The inscribed angle theorem states that the measure of an inscribed angle in a circle equals the twice the measure of the intercepted arc or twice the measure of the central angle.

In the circle given, since the triangle is an equilateral triangle, therefore, all its angles each equals 60°. Therefore:

m(XY) = m(YZ) = m(ZX) = 2(60°) = 120°.

The central angles, m∠XWZ = m∠XWY = m∠YWZ = 120°.

Therefore, the correct measurements are: B. m(arc YZ) = 120°; E. m∠YWZ = 120°.

Learn more about the inscribed angle theorem on:

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