Question

If m∠ADC = 10x - 7 and m∠ABC = 7x + 32, then find the value of x.

A) x = 9.12
B) x = 13
C) x = 3.82
D) x = 2

Answer 1

To find the value of x, the angle measures were set equal to each other, resulting in the equation 10x - 7 = 7x + 32. Solving this equation yields x = 13.

Step-by-step explanation:

The student is asking to find the value of x given that m∠ADC = 10x - 7 and m∠ABC = 7x + 32. This is a typical algebra problem that involves setting two angles equal to each other and solving for x. If the angles ADC and ABC are parts of the same geometric shape, and they are given to be equal, we can set their measures equal to each other and solve the resulting equation:

10x - 7 = 7x + 32

Subtract 7x from both sides:

3x - 7 = 32

Add 7 to both sides:

3x = 39

Divide by 3:

x = 13

Therefore, the correct answer is x = 13, which corresponds with option B).