Question

The figure shows secant GC and tangent GB intersecting to form an angle. Find x and y If necessary, round to the tenths place.

Answer 1

Measure of arc DB = 58°. So ∠ C = 58° : 2 = 29°
Let`s look at the triangle: Δ GBC. GB is a tangent.
29° + 90° + y = 180°
y = 180° - 90° - 29° = 61°
Then ∠ B = 30° : 2 = 15°
In a triangle ΔADC :  ∠ A = 180° - ( 29° + 15° ) = 180° - 44° = 136°
x = 180° - 136° = 44°
Answer: x = 44°,  y = 61°