Question

topic 1: ratio & proportion

1. the ratio of the measures of the angles in a triangle is 8:3:4. find the measures of the angles.

Explanation:

Step1: Define angle variables

Let the angles be $8x$, $3x$, $4x$.

Step2: Sum angles to triangle total

$$8x + 3x + 4x = 180^\circ$$

Step3: Solve for $x$

$$15x = 180^\circ \implies x = \frac{180^\circ}{15} = 12^\circ$$

Step4: Calculate each angle

$8x = 8\times12^\circ = 96^\circ$, $3x = 3\times12^\circ = 36^\circ$, $4x = 4\times12^\circ = 48^\circ$

Answer:

The measures of the angles are $96^\circ$, $36^\circ$, and $48^\circ$.