Question

line segment bd is a diameter of circle e. what is the measure of arc bc? 102°, 30°, 78°, 120°

Explanation:

Step1: Recall inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Angle BDC is an inscribed angle and arc BC is its intercepted arc.

Step2: Find the measure of arc BC

Given that angle BDC = 39°. Let the measure of arc BC be \(x\). By the inscribed - angle theorem, \(m\angle BDC=\frac{1}{2}m\overset{\frown}{BC}\). So, \(39^{\circ}=\frac{1}{2}x\).

Step3: Solve for \(x\)

Multiply both sides of the equation \(39^{\circ}=\frac{1}{2}x\) by 2. We get \(x = 78^{\circ}\).

Answer:

78°