Question

find the value of each variable and the measure of each angle. x = 24 (simplify your answers.) y = 60 find the measure of each angle. (y + x)° = 84° 4x° = 96° (2y - x)° = 96° remaining angle = 96°

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. Given \(4x = 96^{\circ}\), we can solve for \(x\). Since \(4x=96\), then \(x = 24\) (divide both sides by 4: \(x=\frac{96}{4}=24\)).

Step2: Use given \(y\) value to find \((2y - x)\)

We know \(y = 60\) and \(x = 24\). Substitute these values into the expression \(2y - x\). So \(2y-x=2\times60 - 24\).

Step3: Calculate the value of \(2y - x\)

First, calculate \(2\times60=120\). Then \(120-24 = 96\). So the measure of the \((2y - x)^{\circ}\) angle is \(96^{\circ}\).

Answer:

The remaining angle is \(96^{\circ}\)