Question

find the measures of the angles of a triangle whose angles have measures in the ratio 1:2:6.

Explanation:

Step1: Set up the equation

Let the angles be \(x\), \(2x\), and \(6x\). Since the sum of angles in a triangle is \(180^{\circ}\), we have \(x + 2x+6x=180^{\circ}\).

Step2: Solve for \(x\)

Combine like terms: \(9x = 180^{\circ}\). Then \(x=\frac{180^{\circ}}{9}=20^{\circ}\).

Step3: Find the other angles

For the second - angle: \(2x = 2\times20^{\circ}=40^{\circ}\). For the third - angle: \(6x=6\times20^{\circ} = 120^{\circ}\).

Answer:

\(20^{\circ}\), \(40^{\circ}\), \(120^{\circ}\)