Question

Triangle ABC is inscribed in circle L. If angle ACB is 70 degrees and the measure of the intercepted arc AC is 160 degrees, what are the measures of the intercepted arc A, the intercepted arc BC, angle ABC, and angle BAC?

Answer 1

To find the measures of the intercepted arcs and angles in triangle ABC, we can use the properties of inscribed angles and intercepted arcs in a circle.

Step-by-step explanation:

To find the measures of the intercepted arcs and angles in triangle ABC, we can use the properties of inscribed angles and intercepted arcs in a circle.

Given that angle ACB is 70 degrees and the measure of the intercepted arc AC is 160 degrees, we can determine the measures as follows:

1. The measure of intercepted arc A is equal to the measure of angle ACB, which is 70 degrees.
2. The measure of intercepted arc BC is equal to the sum of the measures of intercepted arcs AC and A.
3. The measure of angle BAC is equal to half the measure of the intercepted arc BC.

Using these properties, we can calculate the measures of intercepted arc BC and angle BAC.