Question

use the diagram to complete the statements. the measure of angle ejb is the measure of angle boe. the measure of angle bde is the measure of angle boe. the measure of angle oed is the measure of angle obd. equal to one - half twice 180 minus

Explanation:

Step1: Recall central - inscribed angle relationship

The measure of an inscribed angle is half the measure of the central angle that subtends the same arc. Angle EJB is an inscribed angle and angle BOE is a central angle subtending the same arc $\overset{\frown}{BE}$. So, $\angle EJB=\frac{1}{2}\angle BOE$.

Step2: Recall inscribed - central angle relationship for another pair

Angle BDE is an inscribed angle and angle BOE is a central angle subtending the same arc $\overset{\frown}{BE}$. So, $\angle BDE = \frac{1}{2}\angle BOE$.

Step3: Consider angles in a circle - isosceles triangle property

OB = OD (radii of the circle). In $\triangle OBD$, $\angle OBD=\angle ODB$. In $\triangle OED$, $\angle OED$ and $\angle ODB$ are angles in the same segment of the circle. Also, $\angle OED=\angle OBD$ because angles in the same segment of a circle are equal.

Answer:

The measure of angle EJB is one - half the measure of angle BOE.
The measure of angle BDE is one - half the measure of angle BOE.
The measure of angle OED is equal to the measure of angle OBD.