Question

∠PRQ is inscribed in the arc PRQ of a circle with centre ‘O’.

If ∠PRQ = 75°, then m(arc PRQ) = _______.​

Answer 1

HOPE IT HELPS

THEOREMS USED IN THIS QUESTION IS (INSCRIBED ANGLE THEOREM)

Answer 2

Concept Introduction:-

A spherical shape with no corners or edges is known as circle.

Given Information:-

We have been given that ∠$PRQ$ is inscribed in the arc $PRQ$ of a circle with centre $O$.

To Find:-

We have to find that the value of $m(arc PRQ)$.

Solution:-

According to the problem

The measure of an inscribed angle is half of the measure of the arc intercepted by inscribed angle theorem,

$&\therefore \mathrm{m} \angle \mathrm{PRQ}=\frac{1}{2} \mathrm{~m}(\mathrm{arc} \mathrm{PR}) \\&\therefore \mathrm{m}(\mathrm{arc} \mathrm{PR})=2 \mathrm{~m} \angle \mathrm{PRQ}=2 \times 75^{\circ}=150^{\circ} \\&\therefore \mathrm{m}(\mathrm{arc} \mathrm{PRQ})=360^{\circ}-\mathrm{m}(\mathrm{arc} \mathrm{PR})=360^{\circ}-150^{\circ}=210^{\circ}$

Final Answer:-

The value of $m(\mathrm{arc} \mathrm{PRQ})$ is $210^{\circ}$.