Oak Street and Elm Street run parallel to each other. When Main Street intersects them, it forms interior 26, measuring 70°. What is the measure of
24?

110°

Step-by-step explanation:

The consecutive interior angles theorem states that when two parallel lines are cut by a transversal, the pair of angles formed which lie inside the parallel lines  on the same side of the transversal are known as consecutive interior angles. This consecutive interior angles are supplementary (that is add up to 180°).

Therefore:

∠4 and ∠6 are consecutive interior angles. Hence:

∠4 + ∠6 = 180° (sum of co-interior angles)

∠4 + 70 = 180

∠4 = 180 - 70

∠4 = 110°

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .