Question

please answer friends

Answer 1

given :-

angle PAQ = 35°

O is the center of the circle.

therefore angle POQ = 35 × 2 (angle subtended by same arc on the circle is the half of the angle subtended in the center. therefore angle subtended in the center must be double of the angle subtended by same arc on the circle)

= 70°

now, in ∆POQ,

PO = QO (radii of the same circle)

=> angle OPQ = angle OQP (angle opposite to equal sides)

therefore angle OPQ + POQ + OQP = 180° (angle sum property)

=> angle OPQ + angle OPQ + 70° = 180°

=> 2(angle OPQ) = 180 - 70

=> 2(angle OPQ) = 110°

=> angle OPQ = 110/2

=> angle OPQ = 55°

hence, the measure of angle OPQ is = 55°