Question

In the figure below, BD and EC are diameters of circle P.
What is the arc measure of AE in degrees?

Answer 1

Answer:

27°

Step-by-step explanation:

We know by given

$m \angle APB = 90\°$

$m \angle DPE=63\°$

According to the given circle,

$m\angle DPE + m\angle EPA + m\angle APB=180\°$, by supplementary angles.

Replacing each value, we have

$63\° + m\angle EPA + 90\° = 180\°\\m \angle EPA = 180\° - 153\°\\m \angle EPA = 27\°$

Now, the angle EPA subtends the arc AE, and this angle  is a central angle. So, according to its defintion, the arc AE is equal to its central angle.

$arc(AE)= m\angle EPA = 27\°$

Therefore, the answer is 27°