Question

find the values of x and y.
16.
17.
18.
19.
20.
21.

Explanation:

16.

Step1: Use vertical - angle property

Vertical angles are equal. So, \(16.5x=1.5x + 20\).

Step2: Solve for \(x\)

Subtract \(1.5x\) from both sides: \(16.5x-1.5x=20\), which simplifies to \(15x = 20\). Then \(x=\frac{20}{15}=\frac{4}{3}\).

Step1: Use vertical - angle property

Vertical angles are equal. So, \(6x=15x + 75\).

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(0=15x-6x + 75\), which gives \(9x=-75\), and \(x=-\frac{75}{9}=-\frac{25}{3}\). Also, since \(3y = 15x + 75\), substitute \(x =-\frac{25}{3}\) into it. \(3y=15\times(-\frac{25}{3})+75\).

Step3: Simplify the right - hand side for \(y\)

\(3y=-125 + 75=-50\), then \(y=-\frac{50}{3}\).

Step1: Use vertical - angle property

Vertical angles are equal. So, \(5x=12x - 41\).

Step2: Solve for \(x\)

Subtract \(5x\) from both sides: \(0=12x-5x - 41\), which gives \(7x = 41\), and \(x=\frac{41}{7}\). Also, since \(5y = 5x\), then \(y=x=\frac{41}{7}\).

Answer:

\(x=\frac{4}{3}\)

17.