In the diagram below, a transversal intersects line a and b. a) if m∠1 = 2x+30 and ∠5 = 5x ‒ 45, find the value of x that will make lines a and b parallel. b) tell what definition, postulate or theorem allowed you to solve for x. c) then, find the measure of each angle.

The value of x is 25 and this can be determined by using the corresponding angles property. The measure of angle 1 is 80 degrees and the measure of angle 5 is 80 degrees.

Given :

In the diagram below, a transversal intersects line a and b.

a)

Given :

∠1 = 2x+30 and ∠5 = 5x ‒ 45

Now, the value of 'x' can be calculated as given below:

           (corresponding angles)

2x + 30 = 5x - 45

SImplify the above expression.

75 = 3x

x = 25

b) When the two lines are parallel then the corresponding angles are angle 1 and angle 5.

c)

 (vertical opposite)

 (vertical opposite)

Now, the sum of angle 1 and angle 2 is 180 degrees.

Now, angle 4, angle 6, and angle 8 are equal to 110 degrees.

For more information, refer to the link given below:

link

the equation of the parallel line would be y = 2x + 9

step-by-step explanation:

to start we need to find the slope of the original line. we can do that by looking at the coefficient of x, which is 2

since the slope of the original line is 2 and parallel lines have the same slope, we know the new line will also have 2 slope. now we can use that along with the point given in point-slope form to get the find equation.

y - y1 = m(x - x1)

y - 5 = 2(x + 2)

y - 5 = 2x + 4

y = 2x + 9