Question

AB is a diameter of the circle APBR as shown in the figure. APQ and RBQ are straight lines. Select the statements that are true.

• A. $\therefore \angle PRB={35}^{\circ }$
• B. $\therefore \angle BPQ={90}^{\circ }$
• C. $\angle BPR={30}^{\circ }$
• D. $\angle PBR={115}^o$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A

$\therefore \angle PRB={35}^{\circ }$

B

$\therefore \angle BPQ={90}^{\circ }$

C

$\angle BPR={30}^{\circ }$

D

$\angle PBR={115}^o$

$\angle PRB=\angle BAP$ (Angles in the same segment)

$\therefore \angle PRB={35}^{\circ }$

In $\Delta ABP,\angle APB={90}^{\circ }$ (Angle in semi circle)

$\therefore \angle BPQ={90}^{\circ }$

In $\Delta PQR$

$\angle R+\angle Q+\angle RPQ={180}^{\circ }$

$\Rightarrow {35}^{\circ }+{25}^{\circ }+\angle RPQ={180}^{\circ }$

$\therefore \angle RPQ={180}^{\circ }-{60}^{\circ }={120}^{\circ }$

$\therefore \angle BPR=\angle RPQ-\angle BPQ$

$={120}^{\circ }-{90}^{\circ }={30}^{\circ }$

In $\Delta PBR,$

$\angle PBR={180}^{\circ }-(\angle R+\angle BPR)$

$={180}^{\circ }-({35}^{\circ }+{30}^{\circ })={180}^{\circ }-{65}^{\circ }$

$={115}^{\circ }$