Question

one angle of a triangle measures 100°. the other two angles are in a ratio of 3:5. 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 \(100^{\circ}\), so the sum of the other two angles is \(180 - 100=80^{\circ}\).

Step2: Use the ratio to find the angles

The ratio of the two angles is \(3:5\). Let the angles be \(3x\) and \(5x\). Then \(3x + 5x=80\), which simplifies to \(8x = 80\). Solving for \(x\), we get \(x=\frac{80}{8}=10\).

Step3: Calculate the two angles

Substitute \(x = 10\) into \(3x\) and \(5x\). The first angle is \(3\times10 = 30^{\circ}\) and the second angle is \(5\times10=50^{\circ}\).

Answer:

\(30\) and \(50\)