Question

1. write and solve an equation to find the value of x. then, find the measure of each angle.

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \((2x + 4)+(10x - 4)+(3x)=180\).

Step2: Combine like terms

Combine the \(x\)-terms and constants: \(2x + 10x + 3x + 4 - 4 = 180\) simplifies to \(15x = 180\).

Step3: Solve for \(x\)

Divide both sides by 15: \(x=\frac{180}{15}=12\).

Step4: Find \(\angle V\)

Substitute \(x = 12\) into \(2x + 4\): \(2(12)+4 = 24 + 4 = 28^\circ\).

Step5: Find \(\angle C\)

Substitute \(x = 12\) into \(10x - 4\): \(10(12)-4 = 120 - 4 = 116^\circ\).

Step6: Find \(\angle R\)

Substitute \(x = 12\) into \(3x\): \(3(12)=36^\circ\).

Answer:

\(x = 12\), \(\angle V = 28^\circ\), \(\angle C = 116^\circ\), \(\angle R = 36^\circ\)