Question

Geometry math question no Guessing and Please show work

Answer 1

The lines AB and CD are parallel .

GH is the transversal.

The angles marked 5x-10 and 4x+20 are alternate interior angles.

Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.

When the lines are parallel alternate interior angles are equal.

We can form an equation in x using this property.

5x-10=4x+20

We can solve the equation for x.

For this we bring the x term on one side .To bring x term on same side we subtract 4x both sides

5x-4x-10 =4x-4x+20

Simplifying like terms

x-10=20.

With x we have -10

Adding 10 both sides

x-10+10=20+10

x=30.

Option C is the right answer

Answer 2

The two highlighted angles are alternate interior angles, and as such they have the same measure. This means that

$4x+20=5x-10$

We can easily solve this equation for $x$: start by subtracting $4x$ from both sides:

$20=x-10$

Then add 10 to both sides:

$30=x$