Answer:
(a) 99°
(b) 54°
Step-by-step explanation:
You want the measure of arc PR where 81° external angle PSR is formed by tangents SP and SR. And you want the measure of arc AC intercepted by tangent DA and secant DB that form angle ADB = 53° and intercept arc AB = 160°.
(a) Arc PR
The measure of arc PR is the supplement of the external angle made by the tangents:
PR = 180° -81° = 99°
Arc PR is 99°.
(b) Arc AC
External angle ADB is half the difference of arcs AB and AC, so we have ...
∠D = (AB -AC)/2
2·∠D = AB -AC
AC = AB -2∠D = 160° -2(53°) = 54°
Arc AC is 54°.
