Question

a triangle has an angle that measures 130°. the other two angles are in a ratio of 2:3. 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 \(130^{\circ}\), so the sum of the other two angles is \(180 - 130=50^{\circ}\).

Step2: Use the ratio to find the angles

The ratio of the two angles is \(2:3\). Let the angles be \(2x\) and \(3x\). Then \(2x + 3x=50\), which simplifies to \(5x = 50\). Solving for \(x\), we get \(x=\frac{50}{5}=10\).

Step3: Calculate the individual angles

For the first angle: \(2x = 2\times10 = 20^{\circ}\).
For the second angle: \(3x = 3\times10 = 30^{\circ}\).

Answer:

\(20\) and \(30\)