Question

Angle C is inscribed in circle O. AB start overline, A, B, end overline is a diameter of circle O. What is the measure of \angle B∠Bangle, B?

Answer 1

The measure of ∠angle B when Angle C is inscribed in circle O and AB is a diameter of circle O, is 19 degrees.

What is triangle angle sum theorem?

According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees.

In the image attached below:

• Angle C is inscribed in circle O.
• AB is a diameter of circle O.

The measure of the angle A is,

$m\angle A=71^o$

The measure of the angle C in a semicircle is,

$m\angle C=90^o$

The sum of all the angle(interior) of a triangle is equal to the 180 degrees. Thus,

$\angle A+\angle B+\angle C=180\\90+\angle B+71=180\\\angle B=180-90-71\\\angle B=19^o$

Thus, the measure of ∠angle B when Angle C is inscribed in circle O and AB is a diameter of circle O, is 19 degrees.

Learn more about the triangle angle sum theorem here;

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