Question

10.
(8y + 17)°
(6x - 7)°
(3x - 29)°
11.
(7x - 23)°
49°
(3x)°
(11y - 1)°

Explanation:

Step1: Find the value of \(x\) for problem 10

Since \(l\parallel m\), \((6x - 7)^{\circ}\) and \((3x - 29)^{\circ}\) are consecutive - interior angles.
By the consecutive - interior angles theorem, \((6x - 7)+(3x - 29)=180\).
Combine like terms: \(6x+3x-7 - 29 = 180\), \(9x-36 = 180\).
Add 36 to both sides: \(9x=180 + 36\), \(9x=216\).
Divide both sides by 9: \(x=\frac{216}{9}=24\).

Step2: Find the value of \(y\) for problem 10

Since \(l\parallel m\), \((6x - 7)^{\circ}\) and \((8y + 17)^{\circ}\) are vertical angles.
Substitute \(x = 24\) into \(6x-7\): \(6\times24-7=144 - 7=137\).
Set \(8y + 17=137\).
Subtract 17 from both sides: \(8y=137 - 17\), \(8y=120\).
Divide both sides by 8: \(y=\frac{120}{8}=15\).

Step3: Find the value of \(x\) for problem 11

Since \(49^{\circ}+3x+(7x - 23)=180^{\circ}\) (linear - pair and angle - addition).
Combine like terms: \(49-23+3x + 7x=180\), \(26 + 10x=180\).
Subtract 26 from both sides: \(10x=180 - 26\), \(10x=154\).
Divide both sides by 10: \(x=\frac{154}{10}=15.4\).

Step4: Find the value of \(y\) for problem 11

Since \(3x\) and \((11y - 1)\) are vertical angles.
Substitute \(x = 15.4\) into \(3x\): \(3\times15.4 = 46.2\).
Set \(11y-1 = 46.2\).
Add 1 to both sides: \(11y=46.2 + 1\), \(11y=47.2\).
Divide both sides by 11: \(y=\frac{47.2}{11}\approx4.29\).

Answer:

For problem 10: \(x = 24\), \(y = 15\).
For problem 11: \(x = 15.4\), \(y\approx4.29\).