Question

a triangle has an angle that measures 50°. the other two angles are in a ratio of 4:9. 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 \(50^{\circ}\), so the sum of the other two angles is \(180 - 50=130^{\circ}\).

Step2: Use the ratio to find the angles

The ratio of the two angles is \(4:9\). Let the angles be \(4x\) and \(9x\). Then \(4x + 9x=130\), so \(13x = 130\). Solving for \(x\), we get \(x=\frac{130}{13}=10\).

Step3: Calculate the two angles

The first angle is \(4x = 4\times10 = 40^{\circ}\), and the second angle is \(9x=9\times 10=90^{\circ}\).

Answer:

\(40^{\circ}\) and \(90^{\circ}\)