Question
Consider the circle with center
C
below. What is
m
Q
S
?
Elimination Tool
Select one answer
A
20
∘
B
32.5
∘
C
65
∘
D
155
∘
E
320
∘
C
below. What is
m
Q
S
?
Elimination Tool
Select one answer
A
20
∘
B
32.5
∘
C
65
∘
D
155
∘
E
320
∘
Answers
GPT 3.5
In a circle, the angle made by a chord at the center is twice the angle made by the same chord at the circumference. This is known as the "angle at the center" theorem.
Therefore, if angle QS is given as x degrees, angle CSQ would be 2x degrees.
Since angle CSQ is an exterior angle of the triangle CQS, we have:
2x = m∠CSQ + m∠QCS
2x = 90 + x (since the sum of angles in a triangle is 180 degrees)
x = 90 degrees
Therefore, m∠QS = 90 degrees.
The correct answer is A) 20°.
Therefore, if angle QS is given as x degrees, angle CSQ would be 2x degrees.
Since angle CSQ is an exterior angle of the triangle CQS, we have:
2x = m∠CSQ + m∠QCS
2x = 90 + x (since the sum of angles in a triangle is 180 degrees)
x = 90 degrees
Therefore, m∠QS = 90 degrees.
The correct answer is A) 20°.