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 the equation 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 right - angle property

The angle $(2y + 5)^{\circ}$ and the angle $(5x−17)^{\circ}$ are complementary (since the angle between the two lines is a right - angle, 90 degrees). Substitute $x = 3$ into $(5x−17)$: $5\times3−17=15 - 17=-2$ (this is wrong, we should use the fact that $(2y + 5)+(3x - 11)=90$). Substitute $x = 3$ into the equation: $(2y + 5)+(3\times3 - 11)=90$. First, calculate $3\times3 - 11=9 - 11=-2$. Then the equation becomes $2y+5-2 = 90$, or $2y + 3=90$. Subtract 3 from both sides: $2y=90 - 3=87$. Divide both sides by 2: $y=\frac{87}{2}=43.5$.

Answer:

$x = 3$, $y = 43.5$