Question

Use the image to answer the question.

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.

m∠5=112° and m∠8=(2x+8)° . What equation will solve for x ?

(2 points)
x°+
°=
°

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the value of x, we need to set up an equation using the given information.

From the diagram, we can see that ∠8 and ∠5 are alternate interior angles. Alternate interior angles are congruent when the lines intersected by the transversal are parallel.

Therefore, we have:
∠8 = ∠5

Substituting the given values, we have:
2x + 8 = 112

Simplifying the equation, we can isolate x:
2x = 112 - 8
2x = 104
x = 52

Therefore, the equation that will solve for x is:
2x + 8 = 112

Answer 2

For two vertical angles with measures m∠1=(2x+26)° and m∠3=(3x+32)° , what is the measure of each angle?(1 point)

°