Two intersecting lines create four angles; 1and 3 are a vertical pair. Their sum of their measures is equal to 68°. What equation solves for the value of each angle? (1 point)
Let's call the angles 1, 2, 3, and 4.
Angle 1 and angle 3 are vertical pairs, which means they are congruent. Therefore, angle 1 = angle 3, and we can represent them both as x.
So, angle 1 = x, angle 3 = x.
The sum of the measures of angle 1 and angle 2 is 180° because they are adjacent angles on a straight line. Therefore, angle 2 = 180° - angle 1 = 180° - x.
Similarly, the sum of the measures of angle 3 and angle 4 is 180° because they are adjacent angles on a straight line. Therefore, angle 4 = 180° - angle 3 = 180° - x.
The problem states that the sum of the measures of angle 1 and angle 3 is equal to 68°. So, we can write the equation as:
angle 1 + angle 3 = 68°
x + x = 68°
2x = 68°
Dividing both sides of the equation by 2, we get:
x = 34°
Therefore, angle 1 = angle 3 = 34°, angle 2 = 180° - 34° = 146°, and angle 4 = 180° - 34° = 146°.
Hope this helps!