Question

The horizontal lines (l and m) are parallel. They are crossed by two transversals (lines a and b).

Transversals a and b intersect to make a triangle. The m∠1 = 75°, and the m∠4 = 50°.
1. What is the m∠5? Explain how you know. (2 points)

2. What is the measure of the sum of the angles in a triangle? (2 points)

3. ∠3 is in a triangle with ∠4 and ∠5. Write and solve an equation to find the m∠3. (2 points)

4. What is the measure of a straight angle? (2 points)


5. ∠2 is in a straight line with ∠1 and ∠3. Write and solve an equation to find the m∠2. (2 points)

PLEASE ANSWER! WILL GIVE BRAINLIEST

Answer 1

1. m∠5 = 75° (corresponding angles theorem)

2. 180°

3. m∠3 = 55° (triangle sum theorem).

4. A straight angle = 180°

5. m∠2 = 50° (angles on a straight line)

What is the Triangle Sum Theorem?

According to the triangle sum theorem, the sum of the angles in a triangle equals 180 degrees.

1. m∠5 = m∠1 = 75° (corresponding angles are congruent)

2. Measure of the sum of all angles in a triangle = 180°

3. To find ∠3, we would have the following equation:

m∠3 = 180 - m∠4 - m∠5 (triangle sum theorem).

Substitute and solve

m∠3 = 180 - 50 - 75

m∠3 = 55°

4. A straight angle = 180°

5. m∠2 = 180 - m∠3 - m∠1 (angles on a straight line)

Substitute and solve

m∠2 = 180 - 55 - 75

m∠2 = 50°

Learn more about triangle sum theorem on:

https://brainly.com/question/7696843