Two intersecting lines create four angles; <1 and < 3 are a vertical pair. Their sum of their measures is equal to 68. What equation solves for the value of each angle?

Answer 1

Let's denote the measures of angles <1 and <3 as x and y, respectively. Since angles <1 and <3 are a vertical pair, they are congruent, which means x = y.

The sum of the measures of angles <1 and <3 is equal to 68, so we can write the equation as:
x + y = 68

Since x = y, we can substitute y for x in the equation:
x + x = 68
2x = 68
x = 34

Therefore, the measure of angle <1 (or angle <3) is 34 degrees.

Answer 2

The answers are:

x = 68

68x = 2

2x + 68 = 180

2x = 68

Answer 3

Apologies for the confusion in my previous response.
Let's reconsider the problem.

Let's denote the measures of angles <1 and <3 as x and y, respectively. Since angles <1 and <3 are a vertical pair, they are congruent, which means x = y.

The sum of the measures of angles <1 and <3 is equal to 68, so we can write the equation as:
x + y = 68

Since x = y, we can substitute y for x in the equation:
x + x = 68
2x = 68
x = 34

Therefore, the measure of angle <1 (or angle <3) is 34 degrees.

However, the question asks for an equation that solves for the value of each angle. In this case, the equation would be:
2x = 68

To find the value of x, we can solve the equation by dividing both sides by 2:
x = 68/2
x = 34

Therefore, the measure of each angle, <1 and <3, is 34 degrees.

Answer 4

The sum of the measures of two vertical angles is 300. Solve for the measure of each angle.

answers:

150

75

90

120

Answer 5

Let's denote the measures of the two vertical angles as x and y.

We know that vertical angles are congruent, so x = y.

The sum of the measures of two vertical angles is 300, so we can write the equation as:
x + y = 300

Since x = y, we can substitute y for x in the equation:
x + x = 300
2x = 300
x = 150

Therefore, the measure of each angle, x and y, is 150 degrees.