Questions: Find the value of y.

Find the value of y.
Transcript text: Find the value of $y$.
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Solution

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Solution Steps

Step 1: Find the measure of the central angle

The measure of an inscribed angle is half the measure of its intercepted arc. The inscribed angle that intercepts the arc with measure _z_ has measure 66°. So, the arc has measure 2 * 66° = 132°. The central angle has the same measure as its intercepted arc. So, _z_ = 132°.

Step 2: Find the measure of _x_

Angles _x_, _y_, and _z_ form a full circle, so they add up to 360°. _x_ + _y_ + _z_ = 360° _x_ and _y_ are equal because they intercept congruent arcs and are congruent angles. So, 2_y_ + _z_ = 360° 2_y_ + 132° = 360°

Step 3: Solve for y

2_y_ = 360° - 132° 2_y_ = 228° _y_ = 114°

Final Answer: The value of y is 114°.

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