Question

1. can you set up an equation and solve for x and find the unknown angle measure(s).

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x + 40)+(2x-5)+(3x - 17)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x+40 + 2x-5+3x - 17=(x + 2x+3x)+(40-5 - 17)=6x+18\)

The equation becomes \(6x+18 = 180\)

Step3: Solve for \(x\)

Subtract \(18\) from both sides: \(6x+18-18=180 - 18\), which gives \(6x=162\)

Divide both sides by \(6\): \(x=\frac{162}{6}=27\)

Step4: Find the angle measures

For the first angle: \(x + 40=27+40 = 67^{\circ}\)

For the second angle: \(2x-5=2\times27-5=54 - 5=49^{\circ}\)

For the third angle: \(3x-17=3\times27-17=81 - 17=64^{\circ}\)

Answer:

\(x = 27\), the angle measures are \(67^{\circ}\), \(49^{\circ}\), and \(64^{\circ}\)