Question

Identify the measure of arc RPS. PLEASE HELP!!

Answer 1

Angles TOS and ROQ are congruent, so $m\angle ROQ=m\widehat{RQ}=28^\circ$.

RT is a diameter of the circle, so $m\widehat{RT}=180^\circ$, and in particular

$m\angle ROQ+m\angle QOP+m\angle POT=180^\circ\implies m\angle QOP=62^\circ$

Then

$m\widehat{RPS}=28^\circ+62^\circ+90^\circ+28^\circ=\boxed{208^\circ}$

Answer 2

The measure of arc RPS = $208^{\circ}$.

Measure of arc

The measure of an inscribed angle is half the measure of the intercepted arc.

(The measure of the arc is twice the measure of the angle)

Arc length is a measurement of distance, so it cannot be in radians.

Angles TOS and ROQ are congruent,

so $m \angle R O Q=m \widehat{R Q}=28^{\circ}$.

RT is the diameter of the circle,

so $m \widehat{R T}=180^{\circ}$, and in particular $m \angle R O Q+m \angle Q O P+m \angle P O T=180^{\circ}$

$\Longrightarrow m \angle Q O P=62^{\circ}$

Then

$m \widehat{R P S}=28^{\circ}+62^{\circ}+90^{\circ}+28^{\circ}=208^{\circ}$

$m \widehat{R P S}=208^{\circ}$

The measure of arc RPS = $208^{\circ}$.

Therefore, the correct answer is option (b) $208^{\circ}$.

To learn more about the measure of arc

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