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ankoles [38]
4 years ago
11

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

Mathematics
2 answers:
Ksenya-84 [330]4 years ago
7 0
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
Vikki [24]4 years ago
6 0

Answer: The value of m∠ABC is 102° .

Step-by-step 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.

\frac{m\ CD+m\ DA}{2}=\angle ABC\\\\\frac{128^\circ+76^\circ}{2}=\angle ABC\\\\102^\circ=m\angle ABC

The value of m∠ABC is 102° .

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