Question

In the given figure , find angle OPR​

Answer 1

Answer:

angle OPR = 10°

Step-by-step explanation:

Reflex angle POR = 2 angle PQR

= 2 × 100= 200°

angle POR = 360-200

= 160°

Also,

PO = OR

angle OPR= angle ORP

In ∆ OPR, angle POR = 160°

angle OPR = angle ORP = 10°

Answer 2

Answer:

10°

Step-by-step explanation:

PQR =100°

by theorem angle made by a sector to the center of a circle is double by the angle made by that sector on the circumference of circle

2PQR=reflex POR

2x100°=reflex POR

200°=reflex POR

since,

POR+reflex POR=360°

POR+200°=360°

POR=360°- 200°

POR=160°

And,

POR+OPR+PRO=180°

[OPR+PRO as PO=OR]

160°+2 OPR=180°

2 OPR=180°-160°

2 OPR=20°

OPR=20°/2

OPR=10° ans