Question

1. find the value of x and y. (3x + 8)° (11y + 5)° (4y)° 140° x = y =

Explanation:

Step1: Use angle - equal property

Since the angle \((3x + 8)^{\circ}\) and the \(140^{\circ}\) angle are corresponding angles (assuming the two lines are parallel), we set up the equation \(3x+8 = 140\).
\[3x+8=140\]

Step2: Solve for \(x\)

Subtract 8 from both sides of the equation: \(3x=140 - 8=132\). Then divide both sides by 3, so \(x=\frac{132}{3}=44\).

Step3: Use triangle - angle sum property

In the triangle, the sum of the interior angles is \(180^{\circ}\). So \((11y + 5)+4y+(180 - 140)=180\). First, simplify the left - hand side: \((11y + 5)+4y + 40=180\), which combines to \(15y+45 = 180\).

Step4: Solve for \(y\)

Subtract 45 from both sides: \(15y=180 - 45 = 135\). Then divide both sides by 15, so \(y=\frac{135}{15}=9\).

Answer:

\(x = 44\), \(y = 9\)