Question

the measures of all of the interior angles of a triangle are in the extended ratio 1:2:3. which of the following choices is the value of the smallest angle?
20 degrees
30 degrees
60 degrees
none of the choices are correct.

Explanation:

Step1: Recall triangle angle sum

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

Step2: Define variables from ratio

Given the ratio \(1:2:3\), let the angles be \(x\), \(2x\), and \(3x\).

Step3: Set up equation for angle sum

\(x + 2x + 3x = 180^\circ\)

Step4: Solve for \(x\)

Combine like terms: \(6x = 180^\circ\). Divide both sides by 6: \(x=\frac{180^\circ}{6}=30^\circ\).

Answer:

30 degrees (corresponding to the option "30 degrees")