Question

find the value of x. then find the angle measures of the triangle. sum of angle measures: 180°. 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, \(4x + 40+x=180\).
Combining like - terms, we get \(5x + 40 = 180\).

Step2: Solve for x

Subtract 40 from both sides of the equation: \(5x+40 - 40=180 - 40\), which simplifies to \(5x = 140\).
Then divide both sides by 5: \(x=\frac{140}{5}=28\).

Step3: Find angle measures

The first angle is \(4x\), substituting \(x = 28\), we get \(4\times28 = 112^{\circ}\).
The second angle is \(40^{\circ}\).
The third angle is \(x = 28^{\circ}\).

Answer:

\(x = 28\)
\(28^{\circ},40^{\circ},112^{\circ}\)