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

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

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°.