Question

50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answer 1

There are various components to the given issue. Since angle ACB is a central angle, as explained in the first section, its measure is 72 degrees. Angles ACB and BCD are said to be complementary and form a linear pair in the second section. Thus, 180 - 72 = 108 degrees is the angle BCD's measurement. Following that, it is said that tangents taken from an exterior common point are congruent, causing CR = CP to equal 8 and RB = BQ to equal 4. As a result, QA and PA are both 11. CP and PA added together provide US AC = 19. Finally, we know that angle QPR is 36 degrees according to the inscribed angle theorem.

Answer 2

(B) m∠BCD = 108°

Explanation:

The measure of an arc is equal to the measure of its corresponding central angle. The corresponding central angle of arc AB is angle ACB.

Therefore, if the measure of arc AB is 72°, then m∠ACB = 72°.

Angles on a straight line sum to 180°.

Assuming that AD is a straight line, then:

m∠BCD + m∠ACB = 180°

m∠BCD + 72° = 180°

m∠BCD + 72° - 72° = 180° - 72°

m∠BCD = 108°

Therefore, the measure of angle BCD is 108°.