Question

one angle of a triangle measures 60°. the other two angles are in a ratio of 5:7. 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°. One angle is 60°, so the sum of the other two angles is $180 - 60=120^{\circ}$.

Step2: Set up an equation based on the ratio

Let the two angles be $5x$ and $7x$. Then $5x + 7x=120$. Combining like - terms gives $12x = 120$.

Step3: Solve for x

Dividing both sides of the equation $12x = 120$ by 12, we get $x=\frac{120}{12}=10$.

Step4: Find the measures of the two angles

The first angle is $5x = 5\times10 = 50^{\circ}$, and the second angle is $7x=7\times10 = 70^{\circ}$.

Answer:

50, 70