Question

If mDEF = 124, mDEG = (7x - 9), and mGEF = (5x - 11), find the value of x. Justify your answer.

A) x = 10, by the properties of supplementary angles.
B) x = 20, by the properties of complementary angles.
C) x = 15, by the properties of vertical angles.
D) x = 7, based on the given angle measurements.

Answer 1

To find the value of x, the equation 124 = (7x - 9) + (5x - 11) is formed from the given angles, and solving this gives x = 12. However, this answer doesn't match the given options, indicating a possible error in the question or options.

Step-by-step explanation:

The student is asked to find the value of x based on the given angle measurements of a geometric figure. Since the angles are parts of a larger angle, their measurements can be added together to equal the measurement of the larger angle. The equation can be formed as:

mDEF = mDEG + mGEF

Plugging the given values, we get:

124 = (7x - 9) + (5x - 11)

Solving this equation step by step:

1. Combine like terms: 124 = 12x - 20
2. Add 20 to both sides: 144 = 12x
3. Divide both sides by 12 to get: x = 12

Therefore, the correct value of x is 12, but this option is not given. There might be an error in either the question or the provided options.