Question

a triangle has an angle that measures 50°. the other two angles are in a ratio of 3:10. 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°. One angle is 50°, so the sum of the other two angles is $180 - 50=130^{\circ}$.

Step2: Set up an equation based on the ratio

Let the two angles be 3x and 10x. Then $3x + 10x=130$.
Combining like - terms gives $13x = 130$.

Step3: Solve for x

Dividing both sides of the equation $13x = 130$ by 13, we get $x=\frac{130}{13}=10$.

Step4: Find the measures of the two angles

The first angle is $3x = 3\times10 = 30^{\circ}$.
The second angle is $10x=10\times10 = 100^{\circ}$.

Answer:

30, 100