5. In a triangle, the ratio of the measures of the three angles is 2 : 5 : 8. Find the measure of the smallest angle.

Answer: 24

Step-by-step explanation:

2 : 5 : 8

2x + 5x + 8x = 180 Triangle Sum Theorem

15x = 180

x = 12

The smallest angle is: 2x = 2 (12) = 24

Answer: 24°

Step-by-step explanation: Remember that when the ratio of the angles is 2 : 5 : 8, we can represent the angles as followed.

2x → first angle

5x → second angle

8x → third angle

Now, since the measures of the angles of a triangle add up to 180°, we can set up an equation to represent this.

2x + 5x + 8x = 180

We can simplify on the left side of the equation.

15x = 180

:15 : 15 ← divide both sides by 15

X = 12

Now to find the measure of the smallest angle, we simply plug 12 back in for x. Our first angle 2x measures 2 * 12 which is 24.

Therefore, the smallest angle is 24°.