Question

ZFGH and ZHGJ form a linear pair. Find the measures of the angles if mZFGH = 118° and mZHGJ = (6x - 7).

a) ZFGH = 118°, ZHGJ = 6x - 7°
b) ZFGH = 118°, ZHGJ = 118°
c) ZFGH = 118°, ZHGJ = 6x + 7°
d) ZFGH = 118°, ZHGJ = 7 - 6x°

Answer 1

Angles ZFGH and ZHGJ form a linear pair with measures 118° and (6x - 7). Solving the equation for a linear pair (118° + (6x - 7) = 180°) gives us x = 11.5 and the measure of angle ZHGJ as 62°.

Step-by-step explanation:

The problem states that angles ZFGH and ZHGJ form a linear pair and gives us the measures of the angles as mZFGH = 118° and mZHGJ = (6x - 7). Since ZFGH and ZHGJ form a linear pair, their measures add up to 180° because they are supplementary angles. Using this information, we can set up an equation to find the value of x and thus the measure of angle ZHGJ.

118° + (6x - 7) = 180°

Now solve for x:

1. Add inverse of 118° to both sides of the equation: 6x - 7 = 180° - 118°
2. Simplify the right side: 6x - 7 = 62°
3. Add 7 to both sides: 6x = 69°
4. Divide by 6: x = 11.5°

Substitute x into mZHGJ: mZHGJ = 6(11.5) - 7

mZHGJ = 69 - 7

mZHGJ = 62°

Therefore, the correct measures of the angles are: ZFGH = 118°, ZHGJ = 62°.