Question

find the value of x. then find the angle measures of the triangle. 3x° 40° x° sum of angle measures: 180° x = list the angle measures in order from least to greatest

Explanation:

Step1: Set up equation

The sum of the interior - angles of a triangle is 180°. So, we have the equation \(40 + 3x+x=180\).

Step2: Combine like - terms

Combining the \(x\) terms, we get \(40 + 4x=180\).

Step3: Isolate the variable term

Subtract 40 from both sides: \(4x=180 - 40\), so \(4x = 140\).

Step4: Solve for \(x\)

Divide both sides by 4: \(x=\frac{140}{4}=35\).

Step5: Find the angle measures

One angle is \(40^{\circ}\), another is \(x = 35^{\circ}\), and the third is \(3x=3\times35 = 105^{\circ}\).

Answer:

\(x = 35\)
\(35^{\circ},40^{\circ},105^{\circ}\)