Triangle Angle Theorems Answers

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3

5060✔ 70120

A
50
B
60
C
✔ 70
D
120
111751

⇒ 10

Answer:

111751

111812

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.

Answers:
The measure of angle ABC is °.:60
The measure of angle BAC is °.:50
The measure of angle ACB is °.:70
111813

✔ 506070120

A
✔ 50
B
60
C
70
D
120
111815

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.

Answers:
We know that m∠ZAB + m∠CAB = 180° by the .:angle addition postulate
We also know m∠CAB + m∠ACB + m∠CBA = 180° because .:of the triangle angle sum theorem
Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the .:subtraction property
111816

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

A
they are supplementary angles
B
they are complementary angles
C
✔ of the triangle angle sum theorem
111817

substitution propertyreflexive property✔ subtraction property

A
substitution property
B
reflexive property
C
✔ subtraction property
111820

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

A
Corresponding angles of parallel lines cut by a transversal are congruent.
B
Vertical angles are congruent.
C
Same-side interior angles of parallel lines cut by a transversal are supplementary.
D
Alternate interior angles of parallel lines cut by a transversal are congruent.
111821

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

A
m∠3 + m∠4 = 180°
B
m∠2 + m∠4 + m∠6 = 180°
C
m∠2 + m∠4 = m∠5
D
m∠1 + m∠2 = 90°
E
m∠4 + m∠6 = m∠2
F
m∠2 + m∠6 = m∠5
111822

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.

Answers:
We know that m∠ZAB + m∠CAB = 180° by the .:angle addition postulate
We also know m∠CAB + m∠ACB + m∠CBA = 180° because .:of the triangle angle sum theorem
Therefore, we conclude m∠ZAB = m∠ACB + m∠CBA using the .:subtraction property

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