Question

A. What is the special name for the relationship between angle 2 and angle 5?B. Are angles 2 and 5 congruent, supplementary or complementary?C. If m<1=140, what is m<2? Why?

Answer 1

Given:

In the given diagram, the l and m lines are parallel.

Explanation

a) To find: The special name of the relationship between angles 2 and 5.

We know that,

When two straight lines are cut by a transversal, then the angles formed on the opposite side of the transversal with respect to both the lines are called alternate angles.

So, angles 2 and 5 are alternate interior angles.

b)

Since angles 2 and 5 are alternate interior angles

So, they must be congruent with each other.

Therefore, 2 and 5 are congruent angles.

c) To find: Angle 2 when angle 1 is 140 degrees

Since angles 1 and 2 are linear pairs.

$\begin{gathered} \angle1+\angle2=180 \\ 140+\angle2=180 \\ \angle2=180-140 \\ \angle2=40^{\circ} \end{gathered}$

Therefore, angle 2 is 40 degrees.

Because they are linear pairs.