Question

1. Consider the circle to the right,

Part A: Determine mzSBE.

Part B: Determine mob.

S

52

B

Answer 1

m∠SBE = 26°,
`m\hat O B` = 126°

Explanation:

The arc of a circle is a portion of the circumference of the circle. For a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc.

Central angle is an angle whose vertex is on the center of the circle and endpoints on the circumference of the circle. If the endpoints of the central angle are are also the endpoints for the angle's intercepted arc, then both angles are congruent.

Also, the angle at the center is twice the angle at the circumference.

Angle at center =
`m\hat S E` = 52° (central angle is congruent with angle that intercept the arc)

2 * m∠SBE = central angle (angle at the center is twice the angle at the circumference)

2 * m∠SBE = 52

m∠SBE = 26°

2 * m∠BEO = central angle (angle at the center is twice the angle at the circumference)

2 * 63 = central angle

central angle = 126°

Angle at center =
`m\hat O B` = 126° (central angle is congruent with angle that intercept the arc)