Question

multiple choice 10 points
what is the value of x?

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(3x + 2=(x + 25)+(x + 17)\)

Step2: Simplify the right - hand side of the equation

\((x + 25)+(x + 17)=x+x+25 + 17=2x+42\). The equation becomes \(3x + 2=2x+42\)

Step3: Solve for \(x\)

Subtract \(2x\) from both sides: \(3x-2x+2=2x-2x + 42\), which gives \(x+2=42\). Then subtract 2 from both sides: \(x+2 - 2=42-2\)

Answer:

\(x = 40\)