Question

one angle of a triangle measures 95°. the other two angles are in a ratio of 2:15. what are the measures of those two angles?

Explanation:

Step1: Find the sum of the other two angles

The sum of the interior angles of a triangle is 180°. One angle is 95°, so the sum of the other two angles is $180 - 95=85^{\circ}$.

Step2: Set up an equation based on the ratio

Let the two angles be 2x and 15x. Then $2x + 15x=85$.
Combining like - terms gives $17x = 85$.

Step3: Solve for x

Dividing both sides of the equation $17x = 85$ by 17, we get $x=\frac{85}{17}=5$.

Step4: Find the measures of the two angles

The first angle is $2x = 2\times5 = 10^{\circ}$.
The second angle is $15x=15\times5 = 75^{\circ}$.

Answer:

10 and 75