Question

using angle relationships to find the variable
find the value of x that makes a || b.
(10x - 23)°
137°
a. what is the angle pair relationship?
b. select the correct equation
c. x =

Explanation:

Step1: Identify angle - pair relationship

When two parallel lines \(a\parallel b\) are cut by a transversal, the given angles \((10x - 23)^{\circ}\) and \(137^{\circ}\) are same - side interior angles. For \(a\parallel b\), same - side interior angles are supplementary.

Step2: Set up the equation

Since same - side interior angles are supplementary, we have the equation \((10x-23)+137 = 180\).
Simplify the left - hand side: \(10x+( - 23 + 137)=10x + 114\). So, \(10x+114 = 180\).

Step3: Solve for \(x\)

Subtract \(114\) from both sides of the equation: \(10x+114-114=180 - 114\).
We get \(10x=66\).
Divide both sides by \(10\): \(x=\frac{66}{10}=6.6\).

Answer:

a. Same - side interior angles
b. \((10x - 23)+137 = 180\)
c. \(x = 6.6\)