Question

Line ET is tangent to circle A at T, and the measure of Arc TG is 70°.

What is the measure of ∠GET?

A. 55°
B. 20°
C. 35°
D. 110°

Answer 1

I will calculate this problem in two ways

alternative method 1
we know that
The inscribed angle measures half of the arc it comprises.
∠TNE=(1/2)*arc TG------> (1/2)*70°----> 35°

the triangle TEN is a right triangle
∠TNE+∠GET=90°-----> by complementary angles
∠GET=90-35---> 55°

the answer is
∠GET=55°

alternative method 2
we know that
The measure of the external angle is the semi difference of the arcs that it covers.
∠GET=(1/2)*[arc TN-arc TG]---> (1/2)*[180-70]---> (1/2)*110---> 55°

the answer is
∠GET=55°

Answer 2

Line ET is tangent to circle A at T

∴ ET ⊥ TN
∴ ∠ ETN = 90
the measure of Arc TG = 70

∠ TNG = half the measure of Arc TG = 0.5 *70 = 35

Δ ETN ⇒ The sum of all angles = 180

∴∠ GET = ∠ NET = 180 - (90 + 35 ) = 55


∴ The correct answer is option A. 55°