Emergency: hw due tomorrow
required to write a system of equations
11
find x, y and measurement of angle gfq
12
find x, y and measurement of angle agd

For 11. x = 15 and y = 15 ; ∠GFQ = 45°

Step-by-step explanation:

Work for 11.

Know that when you add ∠GFS ∠QFP ∠PFT to ∠GFQ it should equal 180° because they are supplementary.

(2x + y) + (3x) + (3x + y) + (x + y) = 180

(5x + y) + (4x + 2y) = 180

    9x + 3y = 180

Then add ∠GFQ ∠QFP ∠PFT ∠TFE

(3x) + (3x + y) + (x + y) + (3x) = 180

 (6x + y) + (4x + y) = 180

     10x + 2y = 180

Make the 2 equations equal to each other to find x and y.

9x + 3y = 10x + 2y

- 9x          - 9x

    3y = x + 2y

   - 2y       - 2y

 y = x

Then plug in for y for ∠QFP ∠PFT

(3x + (x)) + (x + (x)) = 90

  4x + 2x = 90

     6x = 90

     x = 15

Then plug in x for ∠GFQ

3(15) = 45

Then to find y you add ∠GFQ and ∠QFS and plug in for x.

45 + (2(15) + y) = 90

45 + 30 + y = 90

    75 + y = 90

  - 75         - 75

          y = 15