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padilas [110]
3 years ago
15

Circle T has diameters RP and QS. The measure of ∠RTQ is 12° less than the measure of ∠RTS.

Mathematics
2 answers:
Olenka [21]3 years ago
7 0

The measure of Arc Q P is 96°. We also know that ∠QTP is central angle, then the measure of arc QP is 96°.

Step-by-step explanation:

<u>Step 1</u>

If QS is a circle diameter,

then m∠QTS=180°.

Let x be the measure of angle RTQ: ∠RTQ =x.

so, let ∠RTQ = x

<u />

<u>Step 2</u>

According to the question,

∠RTQ = ∠RTS - 12°

⇒ ∠RTS = x + 12°

∴ ∠QTS = ∠RTQ + ∠RTS

= x + x + 12° = 2x + 12° = 180°

⇒ 2x = 168°

⇒ x = 84°

⇒ ∠RTQ = 84°

<u></u>

<u>Step 3</u>

Now,

∵∠QTP and ∠RTS are vertical angles

∴ ∠QTP = 84° + 12° = 96°

As ∠QTP is the central angle, hence the measure of arc QP is 96°

<u></u>

<u>Step 4</u>

The Measure of arc QP = 96°

Lena [83]3 years ago
4 0

Answer: 96 is the answer

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