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:

So angle G has measurement 127 degrees.

Step-by-step 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.

Answer 2

Answer: $127^{\circ}$

Step-by-step 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 = $127^{\circ}$