Question

one angle of a triangle measures 95°. the other two angles are in a ratio of 4:13. what are the measures of those two angles? ° and °

Explanation:

Step1: Find the sum of the other two angles

The sum of angles in a triangle is \(180^{\circ}\). One angle is \(95^{\circ}\), so the sum of the other two angles is \(180 - 95=85^{\circ}\).

Step2: Use the ratio to find the angles

The ratio of the two angles is \(4:13\). Let the angles be \(4x\) and \(13x\). Then \(4x + 13x=85\), which simplifies to \(17x = 85\). Solving for \(x\), we get \(x=\frac{85}{17}=5\).

Step3: Calculate the individual angles

For the first angle: \(4x = 4\times5 = 20^{\circ}\).
For the second angle: \(13x=13\times5 = 65^{\circ}\).

Answer:

\(20\) and \(65\)