Question

Angle C is inscribed in circle O. AB is a diameter of circle O. what is angle b

Answer 1

Explanation:

There is no diagram in the question

For the first Diagram

Given

Angle C is inscribed in circle O.

m∠A = 71°

As we know that an angle inscribed in a semicircle is always a right angle.

So from the given diagram,

m∠C = 90°

As we know that the sum of the three interior angles is equal to 180.

so

m∠A + m∠B + m∠C = 180°

71° + m∠B + 90° = 180°

m∠B = 180° - 71° - 90°

m∠B = 19°

Therefore, the measure of m∠B = 19°.

For 2nd Diagram

We can see that angle C is inscribed angle of diameter AB. We know that an inscribed angle whose endpoints are a diameter is a right angle. So measure of angle C will be 90 degrees.

We also know that all angles of a triangle add up-to 180 degrees, so we can set an equation as:

`\angle A+\angle B+\angle C=180^(\circ)46^(\circ)+\angle B+90^(\circ)=180^(\circ)\angle B+136^(\circ)=180^(\circ)\angle B+136^(\circ)-136^(\circ)=180^(\circ)-136^(\circ)\angle B=44^(\circ)`

Therefore, the measure of angle B is 44 degrees.