Question

Given the following diagram, find the required measure.

Given: /llm
m 1 = 140°
m 3 = 50°
21
m 5 =
40
90
50
140

Answer 1

∠ 5 = 40°

Explanation:

∠ 1 and ∠ 2 are adjacent angles and supplementary, thus

∠ 2 = 180° - ∠ 1 = 180° - 140° = 40°

∠ 5 and ∠ 2 are alternate angles and congruent , thus

∠ 5 = 40°

Answer 2

Given that corresponding angles 5 and 3 are supplementary, and angle 3 measures 50 degrees, then angle 5 measures 180-50 = 130 degrees.

In the given diagram, lines l and m are parallel, forming corresponding angles 5 and 3. Corresponding angles are pairs of angles that are on opposite sides of a transversal and are between the two parallel lines. Since the transversal intersects the parallel lines at points A and B, corresponding angles 5 and 3 are supplementary angles, meaning their measures add up to 180 degrees.

We are given that angle 3 measures 50 degrees. Substituting this into the equation for supplementary angles, we get:

m5 + m3 = 180°

m5 + 50° = 180°

m5 = 180° - 50°

m5 = 130°

Therefore, the measure of angle 5 in the diagram is 130 degrees.