Question

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Explanation:

Step1: Use corresponding - angles property

Since the two lines are parallel, the corresponding - angles are equal. The angle of $100^{\circ}$ and the angle $(x - 10)^{\circ}$ are corresponding angles. So we set up the equation $x-10 = 100$.
$x-10=100$

Step2: Solve for $x$

Add 10 to both sides of the equation: $x=100 + 10=110$.

Step3: Use linear - pair property

The angle $(x - 10)^{\circ}$ and the angle $(2y + 24)^{\circ}$ form a linear - pair. Since a linear - pair of angles sums to $180^{\circ}$, and $x = 110$, then the angle $(x - 10)^{\circ}=(110 - 10)^{\circ}=100^{\circ}$. So we have the equation $100+(2y + 24)=180$.
$100+2y+24 = 180$
$2y+124 = 180$

Step4: Solve for $y$

Subtract 124 from both sides: $2y=180 - 124 = 56$. Then divide both sides by 2: $y=\frac{56}{2}=28$.

Answer:

$x = 110,y = 28$