Question

Find the value of each variable. The dot represents the center of the circle. Lines that appear tangent are tangent.

Answer 1

• a° = 26°
• b° = 64°
• c° = 40°

Explanation:

You want the measures of various inscribed angles in the given diagram.

Inscribed angle

The measure of an inscribed angle is half the measure of the arc it intercepts.

Angle a° intercepts an arc of 52°, so ...

a° = 52°/2 = 26°

Angle c° intercepts an arc of 80°, so ...

c° = 80°/2 = 40°

Tangent

The tangent makes a right angle with the diameter, which means that angles a° and b° total 90°.

b° = 90° -a° = 90° -26° = 64°