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.