Question

In the diagram, m CD = 128° and m DA = 76°. What is m∠ABC?

Answer 1

Angle ABC is an inscribed angle.

Inscribed angle = 1/2 * Intercepted Arc

The intercepted arc is arc CD + arc DA, which would be 128 + 76 = 204

m<ABC = 1/2(204)

m<ABC = 102 degrees

You answer is D) 102

Answer 2

Answer: The value of m∠ABC is 102° .

Explanation:

Since we have given that

m CD = 128°

m DA = 76°

We need to find the m∠ABC, Angle subtended at the center is half of the sum of the measure of the arc intercepted by it.

`(m\ CD+m\ DA)/(2)=\angle ABC\\\\(128^\circ+76^\circ)/(2)=\angle ABC\\\\102^\circ=m\angle ABC`

The value of m∠ABC is 102° .