Question

1. one angle of a triangle is twice the size of the second angle, and the third angle is three times the size of the first. what is the size of the smallest angle? 30° 25° 20° 35°

Explanation:

Step1: Define variables

Let the second - angle be \(x\). Then the first - angle is \(2x\), and the third - angle is \(3\times(2x)=6x\).

Step2: Use the triangle - angle - sum formula

The sum of the interior angles of a triangle is \(180^{\circ}\). So \(x + 2x+6x=180^{\circ}\).

Step3: Solve the equation

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

Answer:

\(20^{\circ}\)