Question

1. line segments ad, be, and cf are all diameters of the circle. the measure of angle dof = 130°. determine the measure of ∠boc. explain your thinking.

Explanation:

Step1: Identify vertical angles

$\angle AOB = \angle DOE = 30^\circ$ (vertical angles are congruent)

Step2: Use straight angle property

$\angle DOE + \angle DOF + \angle EOF = 180^\circ$ (angles on a straight line sum to $180^\circ$)
Substitute known values:
$30^\circ + 130^\circ + \angle EOF = 180^\circ$
$\angle EOF = 180^\circ - 30^\circ - 130^\circ = 20^\circ$

Step3: Identify vertical angles

$\angle BOC = \angle EOF = 20^\circ$ (vertical angles are congruent)

Answer:

$\boldsymbol{20^\circ}$