Question

Given: ∠yll ≅ ∠z Prove: m∠1 + m∠2 + m∠6 = 180° a) 2. Angle addition postulate b) 3. Def. of straight angle c) 4. Alternate interior angles theorem d) 8. Substitution

Answer 1

Using the angle addition postulate and substitution property, we can prove that m∡1 + m∡2 + m∡6 = 180°.

Step-by-step explanation:

To prove that m∡1 + m∡2 + m∡6 = 180°, we can use the given information that ∡yll ≅ ∡z.

From the angle addition postulate, we know that ∡yll + ∡z = 180°.

Since ∡yll and ∡z are congruent, we can substitute ∡yll for ∡z to get m∡yll + ∡yll = 180°.

Combining like terms, we have 2m∡yll = 180°, and dividing by 2 gives us m∡yll = 90°.

Therefore, m∡1 + m∡2 + m∡6 = 90° + 90° = 180°.

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