Take Note: Theorem 3-3 Alternate Exterior Angles Theorem

Theorem

If a transversal intersects two parallel lines, then alternate exterior angles are congruent.

If …

l || m l vertical linevertical line m

Then …

∠ 1 ≅ ∠ 7 angle 1 approximately equal to angle 7
∠ 2 ≅ ∠ 8 angle 2 approximately equal to angle 8

Problem 3 Finding Measures of Angles

What are the measures of ∠ 3 angle 3  and ∠ 4 ? angle 4 question mark  Which theorem or postulate justifies each answer?

Image Long Description

Since p || q , m ∠ 3 = 105 p vertical linevertical line q comma m angle , 3 equals 105  by the Alternate Interior Angles Theorem.

Since l || m , m ∠ 4 + 105 = 180 l vertical linevertical line m comma m angle , 4 plus . 105 equals 180  by the Same-Side Interior Angles Theorem. So, m ∠ 4 = 180 − 105 = 75 . m angle , 4 equals 180 , minus . 105 equals 75 .

✓ Got It?

3. Use the diagram in Problem 3. What is the measure of each angle? Justify each answer.
   1. ∠ 1 angle 1
   2. ∠ 2 angle 2
   3. ∠ 5 angle 5
   4. ∠ 6 angle 6
   5. ∠ 7 angle 7
   6. ∠ 8 angle 8