In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°. What is the measure of angle ABC?

Solution:

Given

In Circle D

∠ADC = (7x + 2)°

Arc AC = (8x - 8)°

We have to find the measure of angle ABC.

The measure of an arc is same as the central angle

∠ADC = m arc AC

(7x + 2)° = (8x - 8)°

2 + 8 = 8x - 7x

x = 10°

∠ADC = (70 + 2)° = 72°

∠ACD = 72° = m arc AC

The measure of an inscribed angle is half the measure of its interception.

By using the formula,

∠ABC = 1/2(m arc )

∠ABC = 1/2(m arc AC)

∠ABC = 1/2 × 72°

= 36°

Therefore, ∠ABC = 36°.

In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°. What is the measure of Angle ABC?

Summary:

In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°, the measure of Angle ABC is 36°.