type the correct answer in the box. in triangle abc, which side is the longest if these are the measures of…

Explanation:

Step1: Find the value of x

Since the sum of angles in a triangle is 180°, we have the equation $60+(3x - 2)+(2x + 7)=180$. Combining like - terms: $60+3x-2 + 2x+7=180$, which simplifies to $5x+65 = 180$. Subtract 65 from both sides: $5x=180 - 65=115$. Divide both sides by 5: $x=\frac{115}{5}=23$.

Step2: Find the measures of angles B and C

For angle B: $m\angle B=(3x - 2)^{\circ}$, substituting $x = 23$, we get $m\angle B=(3\times23 - 2)^{\circ}=(69 - 2)^{\circ}=67^{\circ}$. For angle C: $m\angle C=(2x + 7)^{\circ}$, substituting $x = 23$, we get $m\angle C=(2\times23+7)^{\circ}=(46 + 7)^{\circ}=53^{\circ}$.

Step3: Determine the largest angle

Comparing the angles: $m\angle A = 60^{\circ}$, $m\angle B=67^{\circ}$, $m\angle C = 53^{\circ}$. The largest angle is $\angle B$.

Step4: Identify the longest side

In a triangle, the longest side is opposite the largest angle. Since $\angle B$ is the largest angle, the side opposite it is side $AC$.

Answer:

$AC$