Question

a triangle has an angle that measures 20°. the other two angles are in a ratio of 5:11. what are the measures of those two angles? ° and °

Explanation:

Step1: Find the sum of the other two angles

The sum of the interior angles of a triangle is 180°. One angle is 20°, so the sum of the other two angles is $180 - 20=160^{\circ}$.

Step2: Set up an equation based on the ratio

Let the two angles be 5x and 11x. Then $5x + 11x=160$. Combining like - terms gives $16x = 160$.

Step3: Solve for x

Dividing both sides of the equation $16x = 160$ by 16, we get $x=\frac{160}{16}=10$.

Step4: Find the measures of the two angles

The first angle is $5x = 5\times10 = 50^{\circ}$, and the second angle is $11x=11\times10 = 110^{\circ}$.

Answer:

50, 110