The angle measure of arc AC at the center of the circle is; 21°
Circle theorems
From the task content;
- The angle subtended by the arc at the center of the circle is; (3x +9)°
- The angle subtended by the arc on the circumference of the circle is; (3x -1.5)°
It follows that from circle theorems that; The angle subtended by an arc at the center of a circle is twice that which it subtends at the circumference.
Hence;
x = 4.
By substituting x= 4 into the expression; (3x +9)°
Hence, the angle subtended at the center of the circle is; 12+9 = 21°.
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