Question

the angles in a triangle are in the ratio of 1:3:5. find all the angles of the triangle in units of degrees. hint: triangle angles add up to a total of 180 degrees. (10 points)
note: must show setup of linear equation to receive full credit.

Explanation:

Step1: Define variables based on ratio

Let the angles be \( x \), \( 3x \), and \( 5x \) (since the ratio is 1:3:5).

Step2: Set up linear equation

The sum of angles in a triangle is \( 180^\circ \), so \( x + 3x + 5x = 180 \).

Step3: Solve for \( x \)

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

Step4: Find each angle

First angle: \( x = 20^\circ \)
Second angle: \( 3x = 3\times20 = 60^\circ \)
Third angle: \( 5x = 5\times20 = 100^\circ \)

Answer:

The angles of the triangle are \( 20^\circ \), \( 60^\circ \), and \( 100^\circ \).