Triangle Angle Theorems Answers

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⇒ 10

What is the measure of ∠EGF? ° What is the measure of ∠CGF? °

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What is the measure of ∠ABD?

Which represents an exterior angle of triangle XYZ?

Which statement justifies that angle XAB is congruent to angle ABC?

Which statements are always true regarding the diagram? Check all that apply.

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions. The measure of angle ABC is °. The measure of angle BAC is °. The measure of angle ACB is °.

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We start with triangle ABC and see that angle ZAB is an exterior angle created by the extension of side AC. Angles ZAB and CAB are a linear pair by definition. We know that m∠ZAB + m∠CAB = 180° by the . We also know m∠CAB + m∠ACB + m∠CBA = 180° because . Using substitution, we have m∠ZAB + m∠CAB = m∠CAB + m∠ACB + m∠CBA. Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the .

they are supplementary anglesthey are complementary angles✔ of the triangle angle sum theorem

substitution propertyreflexive property✔ subtraction property