Geometry When you find m<8 given m<11=118, which theorem or postulate justifies your answer?
A. Corresponding Angles postulate
B. Alternate Exterior Angels Theorem
C. Alternate Interior Angles Theorem
D. Same-side Interior Angles Theorem

The theorem or postulate that justifies your answer is Alternate Interior Angles Theorem. Option C is correct.

From the given diagram, we are given that m<11 = 118 degrees

To get the measure of angle m<8, we will use the following postulates;

The angle 11 and angle m<12 are supplementary, hence;

m<11 + m<12 = 180

118 + m<12 = 180

m<12 = 180 - 118

m<12 = 62 degrees

The measure of the angle m<11 is also equal to m<8 according to the alternate interior angle theorem. Hence;

m<8 = m<11 = 118 degrees (Alternate Interior Angles Theorem)

Learn more on postulates here:link

Option (C)

Step-by-step explanation:

From the picture attached,

Two lines 'h' and 'k' are the parallel lines and a transversal 'n' is intersecting these parallel lines at two distinct points.

By the theorem of alternate interior angles, angle 8 and angle 11 will be equal in measure.

∠8 ≅ ∠11 [Alternate interior angles]

m(∠8) = m(∠11) = 118°

Therefore, Option (C) will be the answer.

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