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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.

In the diagram below a transversal intersects line a and b a If m1 2x30 and 5 5x 45 find the value of x that will make lines a and b parallel b Tell what defini class=

Respuesta :

wolf1728
When two lines are crossed by a transversal, the lines are parallel if the Alternate Interior Angles are equal. 
Alternate Interior Angles in the diagram are 1 and 5; 4 and 8; 2 and 6 and 3 and 7.
If lines a and b are parallel, then angle 1 must equal angle 5. 
If that's the case then 2x+30 equals 5x ‒ 45
Solving 2x+30 =  5x ‒ 45
3x = 75
x = 25
So, when x = 25, the lines are parallel.

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:

[tex]\angle 1 = \angle 5[/tex]            (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)

[tex]\rm \angle 1 = 2(25) + 30 = 80\; degrees[/tex]

[tex]\rm \angle 3 = 80\; degrees[/tex]  (vertical opposite)

[tex]\rm \angle 5 = 5(25) -45 = 80\; degrees[/tex]

[tex]\rm \angle 3 = 80\; degrees[/tex]  (vertical opposite)

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

[tex]\rm \angle 1 + \angle 2 = 180[/tex]

[tex]\rm \angle 2 = 110\; degrees[/tex]

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

For more information, refer to the link given below:

https://brainly.com/question/10714897

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