Question

1. a triangular playground has angles with measures in the ratio 8:6:4. what is the measure of the smallest angle?

Explanation:

Step1: Find the sum of the ratio parts

The ratio of the angles is \(8:6:4\). The sum of the ratio parts is \(8 + 6+4=18\).

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\).
Let the angles be \(8x\), \(6x\), and \(4x\). Then \(8x + 6x+4x=180^{\circ}\).
Since \(18x = 180^{\circ}\), we can solve for \(x\) by \(x=\frac{180^{\circ}}{18}=10^{\circ}\).

Step3: Find the measure of the smallest angle

The smallest angle is \(4x\). Substitute \(x = 10^{\circ}\) into \(4x\), we get \(4\times10^{\circ}=40^{\circ}\).

Answer:

\(40^{\circ}\)