Question

Find the Measure of BTopic: Inscribed Angles and Central Angles

Answer 1

Answer:

Option B

The measure of angle b is 75°

Step-by-step explanation:

Method 1

we know that

In a inscribed quadrilateral, the opposite angles are supplementary

so

∠a+60°=180° ------> equation A

∠b+105°=180° -----> equation B

To find the measure of angle b solve the equation B

∠b+105°=180°

Subtract 105° both sides

∠b+105°-105°=180°-105°

∠b=75°

Method 2

see the attached figure with letters to better understand the problem

we know that

The inscribed angle measures half that of the arc comprising

so

∠105°=(1/2)[arc ADC]

arc ADC=2*105°=210°

Find the measure of arc ABC

we know that

arc ABC+arc ADC=360° -----> by complete circle

arc ABC=360°-210°=150°

Find the measure of inscribed angle b

∠b=(1/2)[arc ABC]

substitute

∠b=(1/2)[arc 150°]=75°