Question

A circle is shown. Secant R T and tangent U T intersect at point T outside of the circle to form an angle with a measure of 21 degrees. Secant R T intersects the circle at point S. Arc R U is 119 degrees.
What is mArc S U?

49°
77°
98°
161°

Answer 1

Angle formed by a tangent and a secant from an exterior point equals half the difference of the intercepted arcs. So

21 = 1/2 (m arc RU − m arc SU).

Thus m arc SU = m arc RU − 2·21 = 119 − 42 = 77°.

Answer: 77°.