The sizes of the angles are 34° , 44° , 102°
Step-by-step explanation:
The given is:
- The size of the largest angle in a triangle is 3 times the size of the smallest angle
- The third angle is 10° more than the smallest angle
- The size of the third angle is x
We need to find the size of each angle in the triangle
∵ The size of the smallest angle = x°
∵ The size of the largest angle is 3 times the size of the smallest angle
∴ The size of the largest angle = x × 3 = (3x)°
∵ The third angle is 10° more than the smallest angle
∴ The size of the third angle = (x + 10)°
Add the size of the three angles and equate the sum by 180°
∵ The sum of the sizes of the interior angles of a Δ is 180°
∴ x + (3x) + (x + 10) = 180
∴ x + 3x + x + 10 = 180
- Add like terms
∴ 5x + 10 = 180
- Subtract 10 from both sides
∴ 5x = 170
- Divide both sides by 5
∴ x = 34
∵ x is the size of the smallest angle
∴ The size of the smallest angle is 34°
∵ 3x is the size of the largest angle
∴ The size of the largest angle = 3(34) = 102°
∵ x + 10 is the size of the third angle
∴ The size of the third angle = 34 + 10 = 44°
The sizes of the angles are 34° , 44° , 102°
Learn more:
You can learn more about the triangles in brainly.com/question/1479138
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