Question

Circle A is shown. Secant W Y intersects tangent Z Y at point Y outside of the circle. Secant W Y intersects circle A at point X. Arc X Z is 105 degrees and arc W Z is 175 degrees.
In the diagram of circle A, what is the measure of ∠XYZ?

35°
70°
75°
140°

Answer 1

35°

Reason: The angle formed by a tangent and a secant outside a circle equals half the difference of the measures of the intercepted arcs. So ∠XYZ = 1/2(arc WZ − arc XZ) = 1/2(175° − 105°) = 35°.