Angle BAC measures 56°. What is the measure of angle BDC? 
28°, 34°, 56°, 112°

Solution:

Given, angle BAC measures 56 degrees.

We have to find the measure of angle BDC.

We know that angles in the same segment of a circle are equal. In other words, an arc in a circle will subtend equal angles anywhere on the circumference.

Consider the following figure, which shows an arc AB subtending angles ACB and ADB at two arbitrary points C and D on the circumference.

O is the center of the circle. ∠ACB= ∠ADB.

So, angle BAC and BDC have the same arc Bc in the circumference, these angles must be congruent.

So, angle BDC is equal to 56 degrees.

Therefore, ∠BDC = 56°

Angle BAC measures 56°. What is the measure of angle BDC?

Summary:

Angle BAC measures 56°. The measure of angle BDC is 56°.