Question

the ratio of the measures of the angles in a triangle is 8:3:4. find the measures of the angles.
2
smallest angle =
middle angle =
largest angle =

Explanation:

Step1: Find the sum of the ratio parts

The ratio of the angles is \(8:3:4\). First, we find the sum of the parts of the ratio. So, \(8 + 3+4=15\).

Step2: Recall the sum of angles in a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\).

Step3: Find the value of one part

To find the value of one part, we divide the total sum of angles (\(180^{\circ}\)) by the sum of the ratio parts (15). So, \(\frac{180}{15} = 12^{\circ}\) per part.

Step4: Calculate each angle

• Smallest angle: The ratio part for the smallest angle is 3. So, \(3\times12 = 36^{\circ}\)
• Middle angle: The ratio part for the middle angle is 4. So, \(4\times12=48^{\circ}\)
• Largest angle: The ratio part for the largest angle is 8. So, \(8\times12 = 96^{\circ}\)

Answer:

Smallest angle = \(36^{\circ}\)
Middle angle = \(48^{\circ}\)
Largest Angle = \(96^{\circ}\)