The ratios of the measures of the angles of a triangle is 5: 13: 2. find the measures of the angles

 45,  117,18

Step-by-step explanation:

The ratio of the three angles are

5:13:2

Multiply that by x

5x  13x  2x

The sum of the three angles is equal to 180.

5x+13x+2x = 180

Combine like terms

20x = 180

Divide by 20

20x/20 = 180/20

x = 9

The angles are

5x = 5*9 = 45

13x = 13*9 = 117

2x=2*9 = 18

Hello there!

We know that the angles of a triangle have a ratio of:

5:13:2

This means that if we have a variable x, the angles are:

a1 = 5x, a2 =  13x and a3= 2x

We also know that if we add up the 3 angles of a triangle, the result is 180°

this says:

a1 + a2 +a3 = 180°

5x + 13x + 2x = 180°

20x=180°

x = 180°/20 = 9°

now we can replace x in the previous equations and obtain the values of a1, a2 and a3

a1 = 5x = 5*9° = 45°

a2 = 13x = 13*9° = 117°

a3 = 2*9° = 18°

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