Question

Solve for angle..........

Answer 1

57

Explanation:

An angle formed by a tangent and secant is equal to half the difference of its intercepted arcs. ( major arc minus minor arc to be more specific. )

∠B is the angle formed by a tangent and secant

Arc CA is its intercepted arc ( minor arc to be more specific )

Arc DA is also its intercepted arc ( major arc to be more specific )

Hence, ∠B =
`(1)/(2)` ( Arc DA - Arc CA )

If arc CA = 51 and Arc DA = 165

Then ∠B =

`(1)/(2) (165-51)\\165 - 51=114\\(1)/(2) (114)=57`

Hence, ∠B = 57