2 intersecting lines create 4 angles 2 and 4 are a vertical pair. Be some of their measurements are equal to a hundred and ten , which equation will solve for the value of each angle

Answer 1

Let's denote the four angles formed by the intersecting lines as follows: angle 1, angle 2, angle 3, and angle 4.

We are given that angles 2 and 4 form a vertical pair, which means they are congruent. Let's say the measure of angle 2 is x, then the measure of angle 4 is also x.

We are also given that the sum of the measures of angles 2 and 4 is equal to 110 degrees. Therefore, we can write the equation:

angle 2 + angle 4 = 110

x + x = 110

2x = 110

To solve for x, we divide both sides of the equation by 2:

2x/2 = 110/2

x = 55

So, the measure of angle 2 and angle 4 is 55 degrees each.

To find the measures of angle 1 and angle 3, we can use the fact that angles on a straight line add up to 180 degrees. Since angle 2 and angle 4 together form a straight line, we have:

angle 2 + angle 4 + angle 1 + angle 3 = 180

55 + 55 + angle 1 + angle 3 = 180

110 + angle 1 + angle 3 = 180

To solve for the values of angle 1 and angle 3, we subtract 110 from both sides of the equation:

110 + angle 1 + angle 3 - 110 = 180 - 110

angle 1 + angle 3 = 70

Let's say the measure of angle 1 is y, then the measure of angle 3 is also y. We can rewrite the equation:

angle 1 + angle 3 = 70

y + y = 70

2y = 70

To solve for y, we divide both sides of the equation by 2:

2y/2 = 70/2

y = 35

So, the measure of angle 1 and angle 3 is 35 degrees each.