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.

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step-by-step explanation:

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