In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°.
Answers
The complete question is,
In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°. Circle D is shown. Points A, B, and C are on the circle. Point C is on the opposite side of points A and C. Lines are drawn from point A to point B, from point B to point C, from point C to point D, and from point D to point A. What is the measure of Angle A B C ? 36° 43° 72° 144°
Given:
In circle D, angle ADC measures (7x + 2)°.
Arc AC measures (8x - 8)°.
To find:
What is the measure of Angle A B C ?
Solution:
We know that, the measure of an arc is the same as the central angle,, so we have,
∠ ADC = m arc AC
(7x + 2)° = (8x - 8)°
2 + 8 = 8x - 7x
∴ x = 10°
∠ ADC = (7x + 2)° = (7 × 10 + 2)° = 72° = m arc AC
∴ ∠ ADC = 72° = m arc AC
The measure of an inscribed angle is half the measure of its intercepted arc.
we use the formula,
∠ = 1/2 (m arc )
∠ ABC = 1/2 (m arc AC)
∠ ABC = 1/2 × 72° = 36°
∴ ∠ ABC = 36°