Question

one angle of a triangle measures 70°. the other two angles are in a ratio of 4:7. what are the measures of those two angles?

Explanation:

Step1: Find the sum of the other two angles

The sum of angles in a triangle is 180°. One angle is 70°, so the sum of the other two angles is $180 - 70=110^{\circ}$.

Step2: Calculate the measure of the first angle

The ratio of the two angles is 4:7. Let the angles be 4x and 7x. Then $4x + 7x=110$, so $11x = 110$ and $x = 10$. The first angle is $4x=4\times10 = 40^{\circ}$.

Step3: Calculate the measure of the second angle

The second angle is $7x=7\times10 = 70^{\circ}$.

Answer:

40, 70