Answer:
Step-by-step 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:
[tex]\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}[/tex]
Therefore, the measure of angle B is 44 degrees.
