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Chapter 3: Q31. (page 115)

Name or state the postulate, definition, or theorem that justifies each statement about the diagram.

m∠AEB=m∠2+m∠C.

Short Answer

Expert verified

Theorem 3-12 is used to justify the above statement.

Step by step solution

01

Step 1. Find the exterior angle.

Observe that for the triangle ΔBEC, the angle ∠AEBis an exterior angle. The remote interior angles of∠AEBare ∠2 and ∠C.

02

Step 2. Determine the theorem or postulate that can be used.

Theorem 3-12 states that the measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles.

03

Step 3. Apply the theorem.

So, by theorem 3-12, the measure of the exterior angle ∠AEB of the triangleΔBEC equals the sum of the measures of the two remote interior angles which in this case are ∠2 and ∠C.

That is, m∠AEB=m∠2+m∠C.

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