Question

problem 17: (first taught in lesson 18) find x and y. after you enter your answer press go. x = y =

Explanation:

Step1: Sum of angles around a point

The sum of angles around a point is $360^{\circ}$. So $x + 3x+2x + y=360$.

Step2: Simplify the equation

Combining like - terms, we get $6x + y=360$. Also, we can assume that the angles are arranged in a way that $y = 2x$ (by the geometric relationship of the angles in the figure).

Step3: Substitute and solve for x

Substitute $y = 2x$ into $6x + y=360$. We have $6x+2x=360$, which simplifies to $8x = 360$. Then $x=\frac{360}{8}=36$.

Step4: Solve for y

Since $y = 2x$, substituting $x = 36$ gives $y=2\times36 = 72$.

Answer:

$x = 36$, $y = 72$