Question

a certain triangle has interior angle measures of (6x)°, (2x)°, and x°. what is the value of x?
a. 9
b. 12
c. 20
d. 57

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((6x)+(2x)+x = 180\).

Step2: Combine like terms

\(6x+2x + x=(6 + 2+1)x=9x\). So, \(9x = 180\).

Step3: Solve for \(x\)

Divide both sides of the equation \(9x = 180\) by \(9\). We get \(x=\frac{180}{9}=20\).

Answer:

C. \(20\)