The value of x is 70°. The correct option is A. 70
Circle Geometry
From the question, we are to determine the value of the measure of arc x
From one of the circle theorems, we have that
The angle subtended by an arc at the center is twice the angle subtended by it at any point on the circumference.
First, we will determine the value of the third angle in the triangle formed.
Let the angle be y
y + 15° + 20° = 180°
∴ y = 180° - 15° - 20°
y = 145°
Now, the angle supplementary to this is the angle the arc subtends at the circumference.
Thus,
The angle at the circumference = 180° - 145°
The angle at the circumference = 35°
From the above theorem, we can conclude that the angle subtended by the arc at the center of the circle is 2 × 35° = 70°
∴ The measure of the arc is 70°
This is the value of x
Hence, the value of x is 70°. The correct option is A. 70
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