Question

Help pls it’s due soon :/

Chord AB subtends two arcs with measures in the ratio of 1:5. Line PQ is tangent
to the circle at point B. Find the measure of the angle between the tangent and secant AB.

Answer 1

• acute: 30°
• obtuse: 150°

Explanation:

The angle between the secant and the tangent will be half the measure of the intercepted arc. The two intercepted arcs total 1+5=6 ratio units and 360°. That means each ratio unit represents 60° of arc. The two arcs are 60° and 300°.

Then the two angles at the tangent and secant are ...

60°/2 = 30° . . . . . . . the one marked in the attache drawing

300°/2 = 150°