Inscribed Angles in Geometry

In a circle, an angle is formed by two chords that share a common endpoint on the circle. This vertex lies on the circle's edge. Is this type of angle considered an 'inscribed angle'?

• Yes, it is an inscribed angle.

• No, it is a central angle.

• No, it is a circumscribed angle.

• No, it is a tangent angle.

If an inscribed angle intercepts an arc with a measure of 80°, what is the measure of the inscribed angle?

• 160°

• 80°

• 40°

• 20°

An inscribed angle in a circle measures 42°. What is the measure of its intercepted arc?

(a)  

In a circle, a diameter is drawn, and a point on the circle is connected to both ends of the diameter to form an inscribed angle. What is the measure of this angle?

• 45°

• 60°

• 90°

• 180°

Quadrilateral ABCD is inscribed in a circle. If the measure of angle A is 110°, what must be the measure of the opposite angle, angle C?

(a)  

If an inscribed angle is defined by the expression (31x + 3) and it intercepts an arc of 192°, what is the value of x?

• 2

• 3

• 4

• 5

Two inscribed angles in the same circle intercept the exact same arc. What can you conclude about the measures of these two angles?

In a circle, arc BC measures 70° and arc CD measures 122°. If angle CBD is an inscribed angle that intercepts arc CD, what is the measure of angle CBD?

(a)  

A quadrilateral is inscribed in a circle. The measure of one angle is 95°. What is the measure of the angle opposite to it?

• 85°

• 95°

• 180°

• 265°

Explain the relationship between the measure of a central angle and an inscribed angle that intercept the same arc.