Question

10.
(29x - 3)°
(13y - 17)°
(15x + 7)°
l
m
11.

Explanation:

Step1: Solve for \(x\)

Since \((29x - 3)^{\circ}\) and \((15x+7)^{\circ}\) are supplementary angles (they form a linear - pair), we use the equation \(29x-3 + 15x + 7=180\).
Combine like terms: \((29x+15x)+(-3 + 7)=180\), which gives \(44x+4 = 180\).
Subtract \(4\) from both sides: \(44x=180 - 4=176\).
Divide both sides by \(44\): \(x=\frac{176}{44}=4\).

Step2: Solve for \(y\)

Since \(l\parallel m\) (assuming the two lines \(l\) and \(m\) are parallel), \((13y - 17)^{\circ}\) and \((29x - 3)^{\circ}\) are alternate - interior angles. So \(13y-17=29x - 3\).
Substitute \(x = 4\) into the equation: \(13y-17=29\times4-3\).
Calculate \(29\times4-3=116 - 3=113\).
So the equation becomes \(13y-17 = 113\).
Add \(17\) to both sides: \(13y=113 + 17=130\).
Divide both sides by \(13\): \(y=\frac{130}{13}=10\).

Answer:

\(x = 4,y = 10\)