In any triangle, the sum of the angles is 180°. The three angles are represented by the expressions 2x, 3x + 10, and 5x + 40. What are the three angles?

Stuck On a Homework question can anyone help?

The smallest angle is 30 degrees, the second angle is 80 degrees and the third angle is 70 degrees

Step-by-step explanation:

let x = the smallest angle

This means that one angle is x+40, and the third angle is 3x-10. This make our equation:

x + 40 + 3x - 10 + x = 180

Combine like terms

5x + 30 = 180

Subtract 30 from both sides

5x = 150

Divide both sides by 5

x = 30

Plugging this in:

3x - 10 =

90 - 10 =

80

And for the other:

x + 40 =

30 + 40 =

70

Angle 1 - 26 degrees

Angle 2 - 49 degrees

Angle 3 - 105 degrees

Step-by-step explanation:

To answer this, make the equation 2x + (3x + 10) + (5x + 40) = 180. Combine common terms to get: 10x + 50 = 180. Subtract 50 from both sides to get: 10x = 130. Now divide 10 from both sides to get: x = 13.

Now that you have the information x = 13, use it to find the angle measures by inserting the value 13 into the expressions in place of x.

Angle A = 2x:

2x = 2(13) = 26

Angle B = 3x + 10:

3x + 10 = 3(13) + 10 = 39 + 10 = 49

Angle C = 5x + 40:

5x + 40 = 5(13) + 40 = 65 + 40 = 105

Check:

To check your answer, add 26 + 49 + 105. You get 180, so this is correct!

Note:

Hope it helps!

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