Question

a triangle has an angle that measures 50°. the other two angles are in a ratio of 6:7. 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 \(6:7\). Let the angles be \(6x\) and \(7x\). Then \(6x + 7x=130\), which simplifies to \(13x = 130\). Solving for \(x\), we get \(x=\frac{130}{13}=10\).

Step3: Calculate the two angles

Substitute \(x = 10\) into \(6x\) and \(7x\). The first angle is \(6\times10 = 60^{\circ}\) and the second angle is \(7\times10=70^{\circ}\).

Answer:

\(60\) and \(70\)