Questions: Question 5 of 6 If the measures of the angles of a triangle are in the ratio of 2:3:5, then the expressions 2x, 3x, and 5x represent the measures of these angles. What are the measures of these angles? 30°, 55°, 90° 54°, 60°, 60° 30°, 60°, 90° 50°, 65°, 65°

Solution Steps

We are given that the measures of the angles of a triangle are in the ratio of \(2:3:5\). We need to find the actual measures of these angles using the expressions \(2x\), \(3x\), and \(5x\).

Since the sum of the angles in a triangle is \(180^\circ\), we can set up the equation: \[ 2x + 3x + 5x = 180^\circ \]

Combine the terms on the left side: \[ 10x = 180^\circ \] Divide both sides by 10 to solve for \(x\): \[ x = 18^\circ \]

Substitute \(x = 18^\circ\) back into the expressions for the angles:

• First angle: \(2x = 2 \times 18^\circ = 36^\circ\)
• Second angle: \(3x = 3 \times 18^\circ = 54^\circ\)
• Third angle: \(5x = 5 \times 18^\circ = 90^\circ\)

The calculated angles are \(36^\circ\), \(54^\circ\), and \(90^\circ\). None of the provided options exactly match these values. However, the closest match in terms of the largest angle being \(90^\circ\) is:

• \(30^\circ, 60^\circ, 90^\circ\)

Final Answer