Question

Angle 1 and angle 2 form a linear pair. If the measure of angle 1 is (12x+25) degrees and the measure of angle 2 is (3x-10) degrees, find the value of x and the measure of angle 1 and angle 2.

A) x = 5, Angle 1 = 85 degrees, Angle 2 = 5 degrees
B) x = 7, Angle 1 = 99 degrees, Angle 2 = 11 degrees
C) x = 10, Angle 1 = 145 degrees, Angle 2 = 20 degrees
D) x = 15, Angle 1 = 205 degrees, Angle 2 = 45 degrees

Answer 1

By setting up an equation based on the sum of a linear pair of angles being 180 degrees, solving for x yields 11. With x=11, the measures of angle 1 and angle 2 are found to be 157 degrees and 23 degrees, respectively.

Step-by-step explanation:

To find the value of x and the measures of angle 1 and angle 2, we can set up the equation based on the fact that the sum of angles forming a linear pair is 180 degrees. Therefore, the equation is (12x + 25) + (3x - 10) = 180.

Solving the equation:

1. Combine like terms: 12x + 3x + 25 - 10 = 180
2. Simplify: 15x + 15 = 180
3. Subtract 15 from both sides: 15x = 165
4. Divide by 15: x = 11

Now that we have the value of x, we can find the measures of the angles:

• Angle 1 = 12(11) + 25 = 157 degrees
• Angle 2 = 3(11) - 10 = 23 degrees

Therefore, the value of x is 11, the measure of angle 1 is 157 degrees, and the measure of angle 2 is 23 degrees. This means that none of the given options A, B, C, or D are correct.