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Lyrx [107]
1 year ago
14

Circle T is shown. Line segment Q S is a diameters. Point R is opposite of point T. Lines are drawn from points Q and S to point

R to form a right triangle. Angle Q R S is a right angle.
The measure of arc QS is (4x – 18)°.

What is the value of x?
40.5
49.5
94.5
180
Mathematics
1 answer:
Juliette [100K]1 year ago
8 0

The value of angle x of the given cyclic segment is; 49.5°

<h3>How to find the angle of an arc?</h3>

We are given the measure of the angle of  arc QS as (4x – 18)°

Now, to find the measure of arc QS, this angle is to be equal to 180° and as such;

Thus;

(4x – 18)° = 180°

4x - 18 = 180

4x = 180 + 18

4x = 198

x = 198/4

x = 49.5°

The angle subtended by the arc at the center of a circle with center C is the angle of the arc. It is denoted by. m AB, where A and B are the endpoints of the arc. With the help of the arc length formula, we can find the measure of arc angle.

The formula to measure the length of the arc is;

Arc Length Formula (if angle θ is in degrees); s = 2πr (θ/360°)

Arc Length Formula (if θ is in radians) s = ϴ × r.

Thus, the value of x of the given cyclic segment is; 49.5°

Read more about arc angle at; brainly.com/question/2005046

#SPJ1

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