Question

one angle of a triangle measures 115°. the other two angles are in a ratio of 4:9. 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 115°, so the sum of the other two angles is $180 - 115=65^{\circ}$.

Step2: Set up an equation based on the ratio

Let the two angles be 4x and 9x. Then $4x + 9x=65$. Combining like - terms gives $13x = 65$.

Step3: Solve for x

Dividing both sides of the equation $13x = 65$ by 13, we get $x=\frac{65}{13}=5$.

Step4: Find the measures of the two angles

The first angle is $4x = 4\times5 = 20^{\circ}$, and the second angle is $9x=9\times5 = 45^{\circ}$.

Answer:

20, 45