(20 Points) In circle P, M^ ADB is 25°. What is the m^ APB ? ☁︎ A:65 ☁︎ B:40 ☁︎ C:25 ☁︎ D:50

Question

asked Sep 13, 2022 20.6k views

1 Answer

Ashik Abbas · Answer 1 · 2022-09-17T12:01:23+0000

Given:

In circle P, m∠ADB is 25°.

To find:

The m∠APB.

Solution:

Central angle theorem: According to this theorem, the central angle of an arc is twice of inscribed angle of the same arc.

From the given figure it is clear that the ∠APB is the central angle and ∠ADB is the inscribed angle on the arc AB.

By using the central angle theorem, we get

$m\angle APB=2* m\angle ADB$

$m\angle APB=2* (25^\circ)$

$m\angle APB=50^\circ$

Therefore, the correct option is D.