Two straight lines, L_1 and L_2, intersect at point O. One of the angles formed by their i… — GRE General Test

Two straight lines, $L_1$ and $L_2$ , intersect at point $O$ . One of the angles formed by their intersection measures $(3x - 15)^\circ$ , and the vertically opposite angle measures $(x + 25)^\circ$ . What is the degree measure of an angle adjacent to $(3x - 15)^\circ$ ?

A
$20^\circ$
B
$45^\circ$
$135^\circ$ Answer
D
$67.5^\circ$
E
$112.5^\circ$

Answer

135^\circ

Since vertically opposite angles are equal, setting

3x - 15 = x + 25

yields

x = 20

. Substituting

x = 20

into

3x - 15

gives an angle of

45^\circ

. Because adjacent angles on intersecting lines form a straight line (a linear pair), they are supplementary. Therefore, the adjacent angle measures

180^\circ - 45^\circ = 135^\circ

Step-by-Step Solution

Set the vertically opposite angle expressions equal to each other.

3x - 15 = x + 25

Vertically opposite angles formed by two intersecting lines are equal in measure.

Solve for the variable

x

2x = 40 \implies x = 20

Subtract

x

and add

15

to both sides of the equation.

Calculate the degree measure of the angle

(3x - 15)^\circ

3(20) - 15 = 60 - 15 = 45^\circ

Substitute

x = 20

back into the angle expression.

Calculate the measure of an adjacent angle.

180^\circ - 45^\circ = 135^\circ

Adjacent angles along a straight line are supplementary and sum to

180^\circ

Key Concept

Vertically opposite angles are equal, and adjacent angles forming a linear pair are supplementary.

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