Question

Consider the diagram in the picture provided. What is the measure of arc PD?

(A) 35 degrees
(B) 90 degrees
(C) 110 degrees
(D) 180 degrees

Answer 1

Option (C) 110 degrees.

Explanation:

In the given circle if FD is the diameter then as per theorem in Δ FED, ∠FED = 90°

Since ∠ FED = ∠ FEP + ∠ PED

90° = 35° + ∠ PED

∠ PED = 90 - 35

= 55°

In Δ PED⇒ As we know m( arc PD ) = 2 (m ∠ PED)

m( arc PD ) = 2 × 55°

= 110°

therefore, measure of are PD = 110° is the answer.

Option (C) 110° is the answer.

Answer 2

Option C. 110 degrees

Explanation:

In this problem I assume that FD is a diameter

so

arc FP+arc PD=180° ----> because the diameter divide the circle into two equal parts

step 1

Find the measure of arc FP

we know that

The inscribed angle is half that of the arc it comprises.

m<FEP=35°

m<FEP=(1/2)(arc FP)

substitute the values

35°=(1/2)(arc FP)

arc FP=70°

step 2

Find the measure of arc PD

arc FP+arc PD=180°

70°+arc PD=180°

arc PD=180°- 70°=110°