Question

Circle T has diameters RP and QS. The measure of ∠RTQ is 12° less than the measure of ∠RTS. What is the measure of ? 78° 84° 88° 96°

Answer 1

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If QS is a circle diameter, then m∠QTS=180°. Let x be the measure of angle RTQ: m∠RTQ =x.

The measure of ∠RTQ is 12° less than the measure of ∠RTS, then m∠RTS=x+12°.

m∠QTS=m∠RTQ+m∠RTS=x+x+12°=2x+12°=180°,

2x=168°,

x=84°,

m∠RTQ =84°.

The angles ∠QTP and ∠RTS are vertical angles, so m∠QTP=84°+12°=96°.

∠QTP is central angle, then the measure of arc QP is 96°.

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Answer 2

Answer: 96°

Step-by-step explanation:

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