Question

In parallelogram EFGH, the measure of angle F is (3x − 10)° and the measure of angle G is (5x + 22)°. What is the measure of angle G?

Answer 1

Answer:
`127^(\circ)`

Explanation:

Given : In parallelogram EFGH, the measure of angle F is (3x − 10)° and the measure of angle G is (5x + 22)°.

We known that in a parallelogram , the sum of two adjacent angles is 180° .

Therefore , we have

`3x -10+5x + 22=180\\\\\Rightarrow\ 8x+12=180\\\\\Rightarrow\ 8x=180-12\\\\\Rightarrow\8x=168\\\\\Rightarrow\ x=21`

Now, the measure of angle G =
`(5x + 22)^(\circ)=(5(21)+22)^(\circ)=127^(\circ)`

Hence, the measure of angle G =
`127^(\circ)`

Answer 2

So angle G has measurement 127 degrees.

Explanation:

E F

H G

I had to write it out the parallelogram so I could have a better visual.

F and G are consecutive angles in a parallelogram (not on opposite sides).

This means they add to be 180 degrees.

F+G=180

(3x-10)+(5x+22)=180

(3x+5x)+(-10+22)=180

8x +12=180

Subtract 12 on both sides:

8x =180-12

Simplify:

8x =168

Divide both sides by 8:

x =168/8

x =21

If x=21 and want the measurement of angle G, then

(5x+22)=(5*21+22)=127.

So angle G has measurement 127 degrees.