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Leto [7]
3 years ago
5

I need to find angle M

Mathematics
1 answer:
nadezda [96]3 years ago
7 0

Answer:

m<AIR = 90 deg

Step-by-step explanation:

I assume the problem contains an error, and that AR is a diameter, not AC.

Look at the diameter of the circle, AR. It passes through the center of the circle, C. You can think of the two radii of the circle, CR and CA, as sides of angle RCA. Since AR is a diameter, and AR is a segment which is part of line AR, rays CR and CA are sides of an angle that lie on a line. That makes the measure of angle RCA 180 deg. Angle RCA is a central angle of circle C since its vertex is the center of the circle.

Angle AIR is an inscribed angle in circle C since its vertex is on the circle itself. If an inscribed angle and a central angle intercept the circle at the same two points, then the measure of the inscribed angle is half the measure of the central angle.

m<AIR = (1/2)m<RCA = (1/2) * 180 = 90

m<AIR = 90 deg

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The figure is an illustration of the relationship between the angles in a circle and arc

<h3>The measure of angle PSQ</h3>

From the figure, the arc PQ is subtended by the angle PAQ.

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PQ = ∠PAQ

Given that ∠PAQ = 130, it means that:

Arc PQ = 130

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A semicircle measures 180 degrees.

This means that:

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Hence, the measure of QR is 50 degrees

<h3>The measure of arc RS</h3>

The measure of arc RS is then calculated using:

∠RPS = 0.5 * Arc RS ----- inscribed angle is half a subtended angle.

Where ∠RPS = 35

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In (a), we have:

∠PSQ = 65

This means that:

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So, we have:

∠PSB = 65

Next, calculate SBP using:

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So, we have:

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The measure of AQS is then calculated using:

AQS = AQB = 180 - (180 - SBP) - (180 - PAQ)

This gives

AQS = 180 - (180 - 80) - (180 - 130)

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A semicircle measures 180 degrees.

This means that:

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This gives

PS = 180 - RS

Where RS = 70

So, we have:

PS = 180 - 70

Evaluate

PS = 110

Hence, the measure of arc PS is 110 degrees

Read more about circles and arcs at:

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