Question

1. find the values of x and y. (2y + 5)° (5x - 17)° (3x - 11)°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So, $5x−17 = 3x - 11$.

Step2: Solve for $x$

Subtract $3x$ from both sides: $5x-3x−17=3x - 3x-11$, which simplifies to $2x−17=-11$. Then add 17 to both sides: $2x-17 + 17=-11 + 17$, so $2x = 6$. Divide both sides by 2: $x=\frac{6}{2}=3$.

Step3: Use the fact that adjacent angles are supplementary

The angle $(2y + 5)$ and the right - angle ($90^{\circ}$) are adjacent and their sum is $180^{\circ}$ (since they form a straight - line). So, $2y+5+90 = 180$.

Step4: Solve for $y$

First, simplify the left - hand side: $2y + 95=180$. Then subtract 95 from both sides: $2y=180 - 95=85$. Divide both sides by 2: $y=\frac{85}{2}=42.5$.

Answer:

$x = 3$, $y = 42.5$