Answer :
When two lines intersect, they form two pairs of vertical angles. Vertical angles are pairs of opposite angles made by two intersecting lines. Importantly, vertical angles are always congruent, which means they have the same measure.
Given that:
- The measure of [tex]\(\angle 1\)[/tex] is [tex]\(60^{\circ}\)[/tex]
To find the measure of [tex]\(\angle 2\)[/tex]:
1. Identify that [tex]\(\angle 2\)[/tex] is the vertical angle opposite to [tex]\(\angle 1\)[/tex].
2. Since vertical angles are congruent, the measure of [tex]\(\angle 2\)[/tex] will be the same as the measure of [tex]\(\angle 1\)[/tex].
Therefore, since [tex]\(\angle 1\)[/tex] is [tex]\(60^{\circ}\)[/tex], the measure of [tex]\(\angle 2\)[/tex] must also be [tex]\(60^{\circ}\)[/tex].
Hence, the measure of [tex]\(\angle 2\)[/tex] is [tex]\(60^{\circ}\)[/tex].
So, the correct answer is:
[tex]\[ 60^{\circ} \][/tex]
Given that:
- The measure of [tex]\(\angle 1\)[/tex] is [tex]\(60^{\circ}\)[/tex]
To find the measure of [tex]\(\angle 2\)[/tex]:
1. Identify that [tex]\(\angle 2\)[/tex] is the vertical angle opposite to [tex]\(\angle 1\)[/tex].
2. Since vertical angles are congruent, the measure of [tex]\(\angle 2\)[/tex] will be the same as the measure of [tex]\(\angle 1\)[/tex].
Therefore, since [tex]\(\angle 1\)[/tex] is [tex]\(60^{\circ}\)[/tex], the measure of [tex]\(\angle 2\)[/tex] must also be [tex]\(60^{\circ}\)[/tex].
Hence, the measure of [tex]\(\angle 2\)[/tex] is [tex]\(60^{\circ}\)[/tex].
So, the correct answer is:
[tex]\[ 60^{\circ} \][/tex]
