Question

ZEFG and ZGFH are a linear pair, m ZEFG = 4n + 19, and m ZGFH = 3n + 21. What are m ZEFG and m ZGFH?

A. m ZEFG = 3n + 21, m ZGFH = 4n + 19
B. m ZEFG = 4n + 19, m ZGFH = 3n + 21
C. m ZEFG = 4n + 21, m ZGFH = 3n + 19
D. m ZEFG = 3n + 19, m ZGFH = 4n + 21

Answer 1

By setting up an equation based on the given expressions for a linear pair of angles and solving for n, we found m Z E F G to be 99 degrees and m Z G F H to be 81 degrees.

Step-by-step explanation:

The problem involves determining the measures of two angles, Z E F G and Z G F H, which form a linear pair. The measure of angle Z E F G is given as 4n + 19, and the measure of angle Z G F H is 3n + 21. Since they form a linear pair, their measures add up to 180 degrees.

We can set up the equation:
4n + 19 + 3n + 21 = 180
Combining like terms, we have:
7n + 40 = 180
Subtracting 40 from both sides gives us:
7n = 140
Dividing both sides by 7 gives us:
n = 20

Now we can plug in the value of n back into the equations for the measures of Z E F G and Z G F H:
m Z E F G = 4(20) + 19 = 80 + 19 = 99 degrees
m Z G F H = 3(20) + 21 = 60 + 21 = 81 degrees

Thus, m Z E F G = 99 degrees and m Z G F H = 81 degrees.