Question

one angle of a triangle measures 75°. the other two angles are in a ratio of 10:11. 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 75°, so the sum of the other two angles is 180 - 75=105°.

Step2: Set up an equation based on the ratio

Let the two angles be 10x and 11x. Then 10x + 11x=105, which simplifies to 21x = 105.

Step3: Solve for x

Dividing both sides of 21x = 105 by 21 gives x = 5.

Step4: Find the measures of the two angles

The first angle is 10x = 10×5 = 50°. The second angle is 11x = 11×5 = 55°.

Answer:

50, 55