Question

What are the measures of the angles in a triangle with angles in the ratio 3: 5: 10?

A) 18°, 30°, 60°
B) 30°, 50°, 100°
C) 45°, 75°, 150°
D) 60°, 100°, 200°

Answer 1

The angles of a triangle in the ratio 3:5:10 are found by setting up the equation 3x + 5x + 10x = 180, solving for x, and then finding each angle. The resulting angles are 30°, 50°, and 100°.

Step-by-step explanation:

The question is asking for the measures of the angles in a triangle given the ratio of 3:5:10. To solve this, we know that the sum of the angles in any triangle is 180 degrees. Given the ratio, we can assign a variable, let's call it x, to the smallest angle, so the measures of the angles can be represented as 3x, 5x, and 10x. Adding these together gives us:

3x + 5x + 10x = 180

18x = 180

We can then divide both sides by 18 to find the value of x:

x = 10

Now, we can determine the measures of the angles:

• 3x = 3(10) = 30°
• 5x = 5(10) = 50°
• 10x = 10(10) = 100°

Thus, the measures of the angles in the triangle are 30°, 50°, and 100°, which corresponds to option B.