Question

using the figure below. find the value of x and y.
x=
y=
(7y + 27)°
(15x - 5)°
125°

Explanation:

Step1: Find the value of \(x\)

Since \((15x - 5)^{\circ}\) and \(125^{\circ}\) are supplementary angles (they form a linear pair), we use the formula \(a + b=180^{\circ}\).
So, \(15x-5 + 125=180\).
Simplify the left - hand side: \(15x+120 = 180\).
Subtract \(120\) from both sides: \(15x=180 - 120\), \(15x = 60\).
Divide both sides by \(15\): \(x=\frac{60}{15}=4\).

Step2: Find the value of \(y\)

Since the two lines are parallel and the angles \((7y + 27)^{\circ}\) and \((15x - 5)^{\circ}\) are corresponding angles (corresponding angles are equal when two parallel lines are cut by a transversal).
Substitute \(x = 4\) into \((15x - 5)^{\circ}\), we get \(15\times4-5=60 - 5=55^{\circ}\).
Set \(7y+27 = 55\).
Subtract \(27\) from both sides: \(7y=55 - 27\), \(7y = 28\).
Divide both sides by \(7\): \(y=\frac{28}{7}=4\).

Answer:

\(x = 4\)
\(y = 4\)