8. What is m_HTA?
10 points

∠HTA = 62

Step-by-step explanation:

In order to find the measure of ∠HTA we must first find the measure of ∠HAT

∠HAT is an inscribed angle and arc mHT is its intercepted arc

An inscribed angle is equal to half the measure of its intercepted arc

If arc HT = 102° and arc HT is ∠HAT's intercepted arc then ∠HAT = one half of 102

102 / 2 = 51

Hence, ∠HAT = 51°

Now we can calculate the measure of ∠HTA

Angles in a triangle add up to equal 180

Hence, 67 + 51 + ∠HTA = 180

180 - 67 - 51 = 62

Hence, ∠HTA = 62°