Question

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

Explanation:

Step1: Sum angles to 180°

The sum of triangle angles is $180^\circ$, so:
$$(2x+14) + (6x+14) + 64 = 180$$

Step2: Simplify the equation

Combine like terms:
$$8x + 92 = 180$$

Step3: Solve for x

Isolate x by subtracting 92, then divide by 8:
$$8x = 180 - 92 = 88$$
$$x = \frac{88}{8} = 11$$

Step4: Calculate each angle

Substitute $x=11$ into each expression:

• $(2x+14) = 2(11)+14 = 36^\circ$
• $(6x+14) = 6(11)+14 = 80^\circ$
• Given angle: $64^\circ$

Step5: Identify largest angle

Compare the three angle measures: $36^\circ < 64^\circ < 80^\circ$

Answer:

$80^\circ$