When two lines intersect as in the illustration below, four angles are formed. Angles that are side-by-side, such as $\angle 1$ and $\angle 2$ , are called adjacent angles. Angles that are nonadjacent, such as $\angle 1$ and $\angle 3$ or $\angle 2$ and $\angle 4$ , are called vertical angles. From geometry, we know that if two lines intersect, vertical angles have the same measure. If $m ( \angle 1 ) = ( 5 x + 10 ) ^ { \circ }$ and $m ( \angle 3 ) = ( 7 x - 10 ) ^ { \circ }$ , find x . Read $m ( \angle 1 )$ as "the measure of $\angle 1$ ".
A)x = 11
B)x = 15
C)x = 6
D)x = 8
E)x = 10

Question

When two lines intersect as in the illustration below, four angles are formed. Angles that are side-by-side, such as $\angle 1$ and $\angle 2$ , are called adjacent angles. Angles that are nonadjacent, such as $\angle 1$ and $\angle 3$ or $\angle 2$ and $\angle 4$ , are called vertical angles. From geometry, we know that if two lines intersect, vertical angles have the same measure. If $m ( \angle 1 ) = ( 5 x + 10 ) ^ { \circ }$ and $m ( \angle 3 ) = ( 7 x - 10 ) ^ { \circ }$ , find x . Read $m ( \angle 1 )$ as "the measure of $\angle 1$ ". 
A)x = 11 
B)x = 15 
C)x = 6 
D)x = 8 
E)x = 10

Quizplus · Accepted Answer

Since $\angle 1$ and $\angle 3$ are vertical angles, they have the same measure. Setting the two expressions for their measures equal to each other and solving for x, we get: 
$$(5x + 10)^\circ = (7x - 10)^\circ$$
$$5x + 10 = 7x - 10$$
$$20 = 2x$$
$$x = 10$$
Therefore, the answer is choice E.

When Two Lines Intersect as in the Illustration Below, Four ∠1\angle 1∠1

When Two Lines Intersect as in the Illustration Below, Four $\angle 1$