Check for Understanding: Inscribed Triangles, Quadrilaterals

Front

What is the measure of an inscribed angle in relation to its intercepted arc?

Back

The measure of an inscribed angle is half the measure of its intercepted arc.

Front

If angle R is right, what can be said about the triangle inscribed in a circle with diameter SQ?

Back

Angle R is right because the triangle is inscribed and SQ is a diameter.

Front

What is the relationship between the angles in an inscribed triangle?

Back

The opposite angles of an inscribed triangle are supplementary.

Front

How do you find the measure of angle PRQ if the intercepted arc is 102°?

Back

m∠PRQ = 1/2 * m(intercepted arc) = 1/2 * 102° = 51°.

Front

What is the value of x if the angles in a triangle sum up to 180° and two angles are 70° and 60°?

Back

x = 180° - (70° + 60°) = 50°.

Front

What is the definition of an inscribed angle?

Back

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint.

Front

What is the formula to find the measure of an angle formed by two intersecting chords?

Back

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

Front

If the measure of angle A is 40° and angle B is inscribed in the same arc, what is the measure of angle B?

Back

Angle B = 40° (since inscribed angles that intercept the same arc are equal).

Front

What is the relationship between the angles of a quadrilateral inscribed in a circle?

Back

The opposite angles of a cyclic quadrilateral are supplementary.

Front

If the intercepted arc measures 80°, what is the measure of the inscribed angle?

Back

The inscribed angle = 1/2 * 80° = 40°.