Question

a triangle has angles with measures x, 4x, and 10x. find the measure of each angle.
x =
4x =
10x =

Explanation:

Step1: Set up the equation

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

Step2: Combine like terms

Combine \(x\), \(4x\), and \(10x\). We get \(15x = 180\).

Step3: Solve for \(x\)

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

Step4: Find \(4x\)

Substitute \(x = 12\) into \(4x\). \(4x=4\times12 = 48\).

Step5: Find \(10x\)

Substitute \(x = 12\) into \(10x\). \(10x=10\times12=120\).

Answer:

\(x = 12\)
\(4x = 48\)
\(10x = 120\)