Question

triangle abc is shown with the indicated angle measures.
find the measures of the interior angles b and c.
∠b =
∠c =

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, for \(\triangle ABC\), we have \(2x+(x - 2)+86=180\).

Step2: Simplify the equation

Combine like terms: \(2x+x-2 + 86=180\), which simplifies to \(3x+84 = 180\).

Step3: Solve for \(x\)

Subtract \(84\) from both sides: \(3x=180 - 84\), so \(3x=96\). Then divide both sides by \(3\): \(x=\frac{96}{3}=32\).

Step4: Find \(\angle B\)

Since \(\angle B = 2x\), substitute \(x = 32\) into it. So \(\angle B=2\times32 = 64^{\circ}\).

Step5: Find \(\angle C\)

Since \(\angle C=x - 2\), substitute \(x = 32\) into it. So \(\angle C=32-2=30^{\circ}\).

Answer:

\(\angle B = 64^{\circ}\), \(\angle C = 30^{\circ}\)