Question

find the measures of the interior angles of the triangle. a x° (x - 11)° b 73° c ∠a = ° ∠b = ° ∠c =

Explanation:

Step1: Apply angle - sum property of a triangle

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

Step2: Simplify the left - hand side

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

Step3: Solve for \(x\)

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

Step4: Find the measure of each angle

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

Answer:

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