Question

the measures of the angles of a triangle are shown in the figure below. find the measure of the largest angle.

Explanation:

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. So, we set up the equation $(2x + 14)+64+(6x + 14)=180$.

Step2: Combine like - terms

Combining the x - terms and the constant terms, we get $(2x+6x)+(14 + 14+64)=180$, which simplifies to $8x+92 = 180$.

Step3: Solve for x

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

Step4: Find the measure of each angle

The first angle is $2x + 14=2\times11+14=22 + 14 = 36^{\circ}$.
The second angle is 64°.
The third angle is $6x + 14=6\times11+14=66+14 = 80^{\circ}$.

Answer:

$80^{\circ}$