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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鈭�AEB=m鈭�2+m鈭�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 螖BEC, the angle 鈭�AEBis an exterior angle. The remote interior angles of鈭�AEBare 鈭�2 and 鈭燙.

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 鈭�AEB of the triangle螖BEC equals the sum of the measures of the two remote interior angles which in this case are 鈭�2 and 鈭燙.

That is, m鈭�AEB=m鈭�2+m鈭�C.

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