Question

A circle is shown. Secant P N and tangent O N intersect at point N outside of the circle to form an angle with a measure of 45 degrees. The measure of arc M O is 83 degrees.
What is mArc P O ?

128°
173°
192°
256°

Answer 1

Use the exterior-angle formula: an angle formed by a tangent and a secant outside the circle equals half the difference of the intercepted arcs. So

45 = 1/2 |mArc PO − mArc MO|.

Thus 90 = |mArc PO − 83|, giving mArc PO = 173°.