Question

Secant ⎯⎯⎯⎯⎯⎯⎯⎯⎯ and tangent ⎯⎯⎯⎯⎯⎯⎯⎯ intersect outside a circle. The measure of ⏜ is 43° and the measure of ⏜ is 157°.

Determine the measure of ∠ QRS,

Answer 1

∠ QRS = 55°

Explanation:

The tangent- secant angle QRS is half the difference of the intercepted arcs, that is

∠ QRS =
`(1)/(2)` ( RS - PS) =
`(1)/(2)` (157 - 43)° =
`(1)/(2)` × 114° = 57°

Answer 2

57°

Explanation:

∠QRS = (157 - 43) / 2 = 57°