Question

Angle A is represented by the expression 3X + 2. Angle B is represented by the expression X + 10. Angles A and B are vertical angles. What is the sum in degrees of Angle A and Angle B?

A: 28
B: 14
C: 8
D: 4

Answer 1

Vertical angles are congruent, so Angle A and Angle B have the same measure. By solving the equations provided for these angles, we find that each angle measures 14 degrees, making their sum 28 degrees. Therefore, the sum of Angle A and Angle B is 28 degrees, which corresponds to option A.

Step-by-step explanation:

To determine the sum of angles A and B which are vertical angles, we can use the fact that vertical angles are congruent, meaning they have the same measure. Hence, when given expressions for their measures like

Angle A = 3X + 2,
Angle B = X + 10,

we can set them equal to each other because they are vertical angles.

3X + 2 = X + 10 (because Angle A = Angle B)

Solving for X:

3X - X = 10 - 2
2X = 8
X = 4

Now that we have X, we can find the measures of Angle A and B:

Angle A = 3(4) + 2 = 12 + 2 = 14 degrees,
Angle B = 4 + 10 = 14 degrees.

Since vertical angles have the same measure, Angle A and B are both 14 degrees, and thus their sum is:

Angle A + Angle B = 14 + 14 = 28 degrees.

Therefore, the sum of Angle A and Angle B is 28 degrees, which corresponds to option A.