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

Option C. 110 degrees

Step-by-step 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°

Option (C) 110 degrees.

Step-by-step 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.

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