Question

Please help me with geometry

I need help finding the equations to these questions. I don't understand it but I'm required to show work even though we went through all the answers in class. Heres a pic

Answer 1

15. 9 and 54; 16. 14 and 50; 17. 7 and 62;18. 3 and 50

Explanation:

If QR bisects ∠PQS, ∠PQR = ∠RQS

15.

∠PQR = ∠RQS

`\begin{array}{rcl}3x & = & 4x - 9\\0 & = & x - 9\\x & = & \mathbf{9}\\\end{array}`

∠PQS = 2∠PQR = 2 × 27 = 54

16.

∠PQS = 2∠PQR

`\begin{array}{rcl}4x - 6 & = & 2(x + 11)\\4x - 6 & = & 2x + 22\\4x & = & 2x + 28\\2x & = & 28\\x & = & \mathbf{14}\\\end{array}`

∠PQS = 4×14 - 6 = 56 - 6 = 50

17 .

∠PQR = ∠SQR

`\begin{array}{rcl}5x - 4 & = & 3x + 10\\5x & = & 3x + 14\\2x & = & 14\\x&  = & \mathbf{7}\end{array}`

∠PQR = 5×7 - 4 = 35 - 4 = 31

∠PQS = 2∠PQR = 2 × 31 = 62

18.

∠PQR = ∠SQR

`\begin{array}{rcl}8x +1 & = & 6x + 7\\8x & = & 6x + 6\\2x & = & 6\\x  &= & \mathbf{3}\\\end{array}`

∠PQR = 8×3 + 1 = 24 + 1 = 25

∠PQS = 2∠PQR = 2 × 25 = 50