An illustration shows a slanting line intersecting with two lines that appear parallel. The angles that the slanting line forms with the top line are labeled from the top left in a clockwise direction as 1, 2, 4, and 3. The angles that the slanting line forms with the bottom line are labeled from the top left in a clockwise direction as 5, 6, 8, and 7.

Question

m∠1=125° and m∠4=(x+35)°

What equation will solve for x ?

Answer 1

To solve for x, we can use the property that corresponding angles are congruent when two parallel lines are intersected by a transversal.

Given that m∠1 = 125°, we know that m∠5 (the corresponding angle to ∠1) is also 125°.

Similarly, since m∠4 = (x+35)°, we know that m∠8 (the corresponding angle to ∠4) is also (x+35)°.

Therefore, we can set up the equation: m∠5 = m∠8.

Substituting the values we know, we have:

125° = (x+35)°.

To solve for x, we can start by subtracting 35 from both sides:

125° - 35° = x.

Simplifying the left side, we have:

90° = x.

Therefore, the equation to solve for x is x = 90°.