Question

solve for x.
a
c
g
(85 - 2x)°
d
e
h
(93 - 4x)°
b
f
x =

Explanation:

Step1: Use the property of corresponding angles

Since \(CD\parallel EF\), \(\angle CGH\) and \(\angle EHG\) are corresponding angles. And \(\angle CGH=(180-(85 - 2x))^{\circ}=(95 + 2x)^{\circ}\), \(\angle EHG=(93 - 4x)^{\circ}\).
Because corresponding angles are equal when two parallel lines are cut by a transversal, so \(95+2x=93 - 4x\).

Step2: Solve the equation for \(x\)

Add \(4x\) to both sides of the equation: \(95+2x + 4x=93-4x + 4x\), which simplifies to \(95 + 6x=93\).
Subtract \(95\) from both sides: \(6x=93 - 95=-2\).
Divide both sides by \(6\): \(x=\frac{-2}{6}=-\frac{1}{3}\).

Answer:

\(x =-\frac{1}{3}\)