he drawing shows parallel lines r and s intersected by line q.

Question

If m∠3 is 124° and m∠4 = 8x + 40, what is the value of x?

Answer 1

Since line q intersects parallel lines r and s, we can determine that angles 3 and 4 are corresponding angles.

By the Corresponding Angles Postulate, we know that corresponding angles in parallel lines are congruent.

Therefore, m∠3 = m∠4.

Since m∠3 = 124°, we can set up the equation:

124° = 8x + 40.

To solve for x, we need to isolate it on one side of the equation.

Subtract 40 from both sides:

124° - 40 = 8x + 40 - 40.

84° = 8x.

Now to solve for x, divide both sides by 8:

84°/8 = 8x/8.

10.5° = x.

Therefore, the value of x is 10.5°.