Angles, Tangents, and Secants in Circles

What is the formula to use when solving for arcs/angles in circles with intersecting chords?

Find the measure of the missing angle in degrees. (Hint: Intersecting Chords)

• 79

• 57

• 22

• 83

Find the measure of the missing arc in degrees. (Hint: Intersecting Chords)

• 103

• 16

• 71

• 94

If a polygon is circumscribed around a circle, then all sides are_.

• Tangent

• Secant

• Supplementary

• Complimentary

• Congruent

If a tangent and a secant, two secants, or two tangents intersect in a point in the exterior of a circle, then the measure of the angle formed is equal to one-half the ____________ of the measures of the intersected arcs.

• difference

• sum

• twice

• half

The measure of arc HJ = 110 degree and arc LJ = 150 degree, what is the measure of angle K?

Quadrilateral LOVE is inscribed in the circle as shown. If the measure of angle V = 140 degree, what is the measure of arc ELO?

• 140⁰

• 80⁰

• 280⁰

• 40⁰

In a circle, a diameter bisects a chord and an arc with the same endpoints if and only if it is __________ to the chord.

• parallel

• congruent

• perpendicular

• bisect

If a quadrilateral is inscribed in a circle, then its opposite angles are ___________.

• complementary

• supplementary

• congruent

• bisect

If two chords intersect within a circle, then the measure of the angle formed is equal to half the ______ of the measures of the intercepted arcs.

• measures

• sum

• twice

• half