Question

look at the diagram.
which equation can be used to solve for x?
22x + 36 = 128
22x - 36 = 128
5x - 19 = 128
5x + 53 = 128
solve for x.
x =

Explanation:

Step1: Use the exterior - angle theorem for angles formed by two rays and a transversal

The exterior - angle theorem for angles formed by two rays and a transversal states that the measure of an exterior angle is equal to the sum of the measures of the two non - adjacent interior angles. Here, \(128^{\circ}=(5x + 17)^{\circ}+36^{\circ}\).

Step2: Simplify the equation

First, simplify the right - hand side of the equation: \((5x + 17)+36=5x+(17 + 36)=5x+53\). So the equation becomes \(5x+53 = 128\).

Answer:

The equation \(5x + 53=128\) can be used to solve for \(x\).
Now, solve for \(x\):

Step1: Subtract 53 from both sides of the equation

\(5x+53-53=128 - 53\).
\(5x=75\).

Step2: Divide both sides by 5

\(x=\frac{75}{5}=15\).
So \(x = 15\).