Question

Angle BCDSBC equals PDM angle B equals 13 X -35 M angle C equals 5X -19, and M angle D equals 2X +14. Find X and the measure of each angle.

A. X = 12, B = 139°, C = 41°, D = 38°
B. X = 10, B = 125°, C = 31°, D = 32°
C. X = 9, B = 104°, C = 26°, D = 30°
D. X = 14, B = 152°, C = 51°, D = 28°

Answer 1

To solve for x and the angles, the student must set up a system of equations based on the sum of angles in a triangle being 180 degrees and then solve for x using algebraic methods.

Step-by-step explanation:

The student is asking for the solution to a system of equations involving multiple angles in a geometric context. To find the value of x and the measurements of each angle, we need to apply the fact that the sum of the angles in a triangle is 180 degrees. In the provided problem, we can assume there's a triangle with angles B, C, and D.

We have the following equations:

M angle B = 13x - 35

M angle C = 5x - 19

M angle D = 2x + 14

Adding these together and setting the sum equal to 180° gives:

(13x - 35) + (5x - 19) + (2x + 14) = 180

Solving this equation for x and then substituting it back into the original equations will give us the measures of angles B, C, and D.