Geometry-Angles in a Circle

Front

What is the measure of an angle formed by two chords intersecting inside a circle?

Back

The measure of the angle is equal to half the sum of the measures of the arcs intercepted by the angle.

Front

If arc VY = 132° and ∠ YUV = 41°, what is the measure of arc XV?

Back

50°

Front

If arc XV = 68° and ∠ YUV = 36°, what is the measure of arc VY?

Back

140°

Front

What is the relationship between the angles of a cyclic quadrilateral?

Back

The opposite angles of a cyclic quadrilateral are supplementary (they add up to 180°).

Front

If arc AB = 70°, how many degrees are in ∠ ADB?

Back

35°

Front

What is the measure of an angle formed by a tangent and a chord through the point of contact?

Back

The measure of the angle is equal to half the measure of the intercepted arc.

Front

If arc SQ = 92° and arc QR = 86°, what is the measure of ∠ RPS?

Back

45°

Front

What is the measure of an inscribed angle?

Back

An inscribed angle is half the measure of the intercepted arc.

Front

If m∠ A = 95° in a cyclic quadrilateral ABCD, what is the measure of m∠ C?

Back

m∠ C = 85°.

Front

What is the formula for finding the measure of an angle formed by two secants intersecting outside a circle?

Back

The measure of the angle is equal to half the difference of the measures of the intercepted arcs.