Question

a triangle has angles in the ratio 2 : 3 : 4. what is the measure of the largest angle of the triangle?
a 40°
b 60°
c 80°
d 120°

Explanation:

Step1: Set up the angle expressions

Let the angles be $2x$, $3x$, and $4x$.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $2x + 3x+4x=180^{\circ}$.
Combining like - terms gives $9x = 180^{\circ}$.
Solving for $x$: $x=\frac{180^{\circ}}{9}=20^{\circ}$.

Step3: Find the measure of the largest angle

The largest angle is $4x$. Substituting $x = 20^{\circ}$, we get $4\times20^{\circ}=80^{\circ}$.

Answer:

C. $80^{\circ}$