Question

Given that QRST is a parallelogram, find the angle measures:

Answer 1

Angle R is 127 degrees and Angle S is 53 degrees

Explanation:

We know that adjacent angles in a parallelogram are supplementary, meaning that they add up to 180 degrees.

With this, we can create an equation to solve for x with the values given for Q and T

Q+T = 180

(3x+5)+(9x-17) = 180

12x -12 = 180

12x = 192

x = 16

Now we can find the angles of Q and T given the value of x

Q = (3x+5)

Q = (3*16+5)

Q = 53 degrees

T = (9x-17)

T = (9*16-17)

T = 127 degrees

Since opposite angles in a parallelogram are congruent,

angle S = angle Q and angle R = angle T

Answer 2

below

Explanation:

consecutive angles are supplementary in parallelogram

q+t = 180

3x+5+9x-17 = 180

12x-12 = 180

x-1 = 15

x=16

r=t = 127°

q=s = 53°