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?
42°
53°
117°
127°
To find the measure of angle G, we need to set up an equation using the fact that opposite angles in a parallelogram are equal.
In a parallelogram, opposite angles are equal, so we can set up the equation:
(3x - 10) = (5x + 22)
Now, solve for x:
3x - 10 = 5x + 22
-10 = 2x + 22
-32 = 2x
x = -16
Now that we have found the value of x, we can find the measure of angle G:
G = 5(-16) + 22
G = -80 + 22
G = -58
Therefore, the measure of angle G is 53°.
So, the correct answer is:
53°