Geometry- Triangle Angle Theorems assignment

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

-m∠3 + m∠4 = 180° -m∠2 + m∠4 + m∠6 = 180° -m∠2 + m∠4 = m∠5

What is the value of k?

10

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 _____.

60 50 70

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

65 115

What is the value of x?

98

Given: ΔABC Prove: m∠ZAB = m∠ACB + m∠CBA 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 _____.

angle addition postulate of the triangle angle sum theorem subtraction property

What is the measure of ∠ABD?

c. 114

Which represents an exterior angle of triangle XYZ?

c. JXZ

Given: m || CB Prove: m∠ABC + m∠BAC + m∠ACB = 180° Which statement justifies that angle XAB is congruent to angle ABC?

d. Alternate interior angles of parallel lines cut by a transversal are congruent.