Question

1. the figure shown is not drawn to scale. a. what is the value of x? b. what is the value of y?

Explanation:

Step1: Use angle - relationship

Since $(3x - 10)^{\circ}$ and $(x + 100)^{\circ}$ are vertical angles, they are equal. So we set up the equation $3x-10=x + 100$.

Step2: Solve the equation for x

Subtract $x$ from both sides: $3x-x-10=x - x+100$, which simplifies to $2x-10 = 100$. Then add 10 to both sides: $2x-10 + 10=100 + 10$, getting $2x=110$. Divide both sides by 2: $x=\frac{110}{2}=55$.

Step3: Find the value of y

We assume that the angle marked $y^{\circ}$ and the angle adjacent to $(x + 100)^{\circ}$ are corresponding angles or equal - related angles. First, when $x = 55$, $x + 100=55+100 = 155$. If we assume the angle adjacent to $(x + 100)^{\circ}$ and $y^{\circ}$ are equal (depending on the parallel - line relationship in the figure), then $y$ is found by considering the linear - pair or other angle relationships. But if we assume the two horizontal lines are parallel and use the corresponding - angle property, we need more information about the figure's angle - relationships. However, if we assume that the angle adjacent to $(x + 100)^{\circ}$ and $y^{\circ}$ are equal, and since the angle adjacent to $(x + 100)^{\circ}=180-(x + 100)$. When $x = 55$, this adjacent angle is $180-(55 + 100)=25$. So if $y$ is equal to this adjacent angle (by corresponding - angle or equal - angle relationship), $y = 25$.

Answer:

a. $x = 55$
b. $y = 25$