Question

in the adjoining figure P is the center if AD=DB, then what is the measure of angle x

Answer 1

Answer:

30

Step-by-step explanation:

Comparing triangles APD and BPD,

AD = DB (given)

PD common side

AP = PB(radius of the circle).

Hence , both triangle APD and BPD are congruent.

∠ADP = ∠BDP

But ∠ADP + ∠BDP = 180°

=> ∠ADP = ∠BDP = 90°

∠APD = ∠BPD (due to congruency)

Thus, ∠APB = 60°.

If a chord subtends an angle 2∅ at the center of the circle, it will subtend an angle ∅ at any point on the circle on the same segment.

Hence x = 30°.