Question

∠1 and ∠3 are remote interior angles of ∠5 .∠1 and ∠2 are remotae interior angles of ∠_. ∠2 and ∠3 are remote interior angles of ∠_.

Answer 1

Remote interior angles in a triangle are equal in measure.

Step-by-step explanation:

Remote interior angles are angles inside a triangle that are not adjacent to a given angle. In this case, ∠1 and ∠3 are remote interior angles of ∠5, and ∠1 and ∠2 are remote interior angles of ∠_, and ∠2 and ∠3 are remote interior angles of ∠_.

Remote interior angles are equal in measure, meaning that ∠1 = ∠3, ∠1 = ∠2, and ∠2 = ∠3.

For example, if ∠1 is 30 degrees, then ∠3 will also be 30 degrees, and ∠2 will also be 30 degrees.

Answer 2

a = ∠2 = 90° and b = 90°.

In a set of parallel lines cut by a transversal, remote interior angles are supplementary. So, we can use this property to find the values of
`\(a\) and \(b\)`.

Given:

1. ∠1 and ∠3 are remote interior angles of ∠5:

∠1 + ∠3 = 180°

2. ∠1 and ∠2 are remote interior angles of ∠a:

∠1 + ∠2 = 180°

3. ∠2 and ∠3 are remote interior angles of ∠b:

∠2 + ∠3 = 180°

Now, let's solve for
`\(a\) and \(b\)`:

From equation (1):

∠1 + ∠3 = 180°

From equation (2):

∠1 + ∠2 = 180°

Subtracting equation (2) from equation (1) to eliminate ∠1:

(∠1 + ∠3) - (∠1 + ∠2) = 180° - 180°

∠3 - ∠2 = 0

∠3 = ∠2

So, a = ∠2.

Now, let's consider equation (3):

∠2 + ∠3 = 180°

Since we know ∠3 = ∠2, we can substitute:

∠2 + ∠2 = 180°

2∠2 = 180°

∠2 = 90°

So, b = 90°.

Complete the question:

∠1 and ∠3 are remote interior angles of ∠5 .∠1 and ∠2 are remote interior angles of ∠a. ∠2 and ∠3 are remote interior angles of ∠b. find values of a and b.