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AURORKA [14]
3 years ago
14

Multiple choice, please help

Mathematics
1 answer:
Marina86 [1]3 years ago
5 0
I think it A but I’m not 100% sure
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Angle ABC is inscribed in a circle as shown.<br><br>What is the measure, in degrees, of angle ABC?
sladkih [1.3K]

Answer

Find out the measure, in degrees, of angle ABC .

To prove

The relationship between inscribed angles and their arcs

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

The formula is  

Measure\ of\ inscribed\ angle = \frac{1}{2}\times measure\ of\ intercepted\ arc

As given in the diagram

The measure of the intercepted arc A to B is 120°.

Put value in the formula

\angle ABC = \frac{1\times 120^{\circ}}{2}

∠ABC = 60°

Therefore the measure of the ∠ABC is 60° .


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AD←→ is tangent to circle M at point D. The measure of ∠DMQ is 58º.
Marat540 [252]

Answer:

32°

Step-by-step explanation:

Given:

∠DMQ = 58º

In this circle, the radius is DM. Since AD is tangent to the circle M, at point D, and the angle between a tangent and a radius is 90°

Therefore, ∠MDQ = 90°

The total angle in a triangle is 180°. Since we have the values of ∠MDQ and ∠DMQ, ∠DQM will be calculated as:

180 = ∠DMQ + ∠MDQ + ∠DQM

Solving for ∠DQM, we have:

∠DQM = 180 - ∠DMQ - ∠MDQ

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The measure of ∠DQM is 32°

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2 years ago
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