Question

Find the measure of angles 1 and 2.

Explain your reasoning as to how you determined the measurements of angles 1 and 2.

Answer 1

The measure of angles 1 and 2 is 135 degrees and 45 degrees respectively.

The pairs of angles inside the two lines and on either side of a transversal that cuts across two lines are referred to as alternate internal angles.

Measurement of angle 1 is equal to 135° as it is an alternate internal angle.

m∠ 1 = 135°

we know that ∠ 1 and ∠ 2 are supplementary angles.

This means that

∠ 1 + ∠ 2=180°

Substituting the angle 1 value

135° + m ∠ 2 = 180°

m ∠ 2 = 180° - 135°

m∠ 2 = 45°

Answer 2

Answer:
m<1 = 135°
m<2 = 135°

Explanation:

When solving for angles we know that the horizontal lines are both parallel. This means that 135° is equal to number 1.

For angle 2 we know that angles opposite are equal to the angle already given. This means that angle 2 is equal to angle 1.

The image I gave should help you understand this.