Question

question
the measures of the angles of a triangle are shown in the figure below. find the measure of the largest angle.
(2x+14)°
(6x+14)°
64°

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \((2x + 14)+(6x + 14)+64 = 180\).

Step2: Simplify the equation

Combine like terms: \(8x + 92 = 180\).

Step3: Solve for \(x\)

Subtract 92 from both sides: \(8x = 180 - 92 = 88\). Then divide by 8: \(x=\frac{88}{8}=11\).

Step4: Find each angle

• First angle: \(2x + 14 = 2(11)+14 = 36^\circ\).
• Second angle: \(6x + 14 = 6(11)+14 = 80^\circ\).
• Third angle: \(64^\circ\).

Step5: Identify the largest angle

Compare \(36^\circ\), \(80^\circ\), and \(64^\circ\). The largest is \(80^\circ\).

Answer:

\(80^\circ\)