Question

9.6
score: 12.67/15 answered: 12/15
question 12
one angle in a triangle measures twice the smallest angle, whereas the largest angle is six times the smallest angle. find the measures of all three angles.
the smallest of the angles is degrees, the middle angle is degrees, and the largest is degrees.
question help: video message instructor

Explanation:

Step1: Set up the equation

Let the smallest angle be \(x\) degrees. Then the middle - sized angle is \(2x\) degrees and the largest angle is \(6x\) degrees.
Since the sum of the interior angles of a triangle is \(180^{\circ}\), we have the equation \(x + 2x+6x=180\).

Step2: Solve the equation for \(x\)

Combine like terms: \(9x = 180\).
Divide both sides by 9: \(x=\frac{180}{9}=20\).

Step3: Find the other two angles

The middle - sized angle: \(2x = 2\times20 = 40\).
The largest angle: \(6x=6\times20 = 120\).

Answer:

The smallest of the angles is \(20\) degrees, the middle angle is \(40\) degrees, and the largest is \(120\) degrees.