Question

find the measures of the interior angles of the triangle
∠a = □°
∠b = □°
∠c = □°

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(x+(x - 11)+73=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x+x)+(-11 + 73)=180\), which gives \(2x+62 = 180\).

Step3: Solve for \(x\)

Subtract 62 from both sides: \(2x=180 - 62\), so \(2x=118\). Then divide both sides by 2: \(x=\frac{118}{2}=59\).

Step4: Find the measure of \(\angle B\)

Substitute \(x = 59\) into \((x - 11)\). So, \(\angle B=(59 - 11)^{\circ}=48^{\circ}\).

Step5: Identify the angles

\(\angle A=x^{\circ}=59^{\circ}\), \(\angle B=(x - 11)^{\circ}=48^{\circ}\), \(\angle C = 73^{\circ}\).

Answer:

\(\angle A = 59^{\circ}\), \(\angle B=48^{\circ}\), \(\angle C = 73^{\circ}\)