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 an

Question

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

work out the size, in degrees, of each angle in the triangle.
You must show your working (let X be the smallest angle).​

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Skylar 2 days 2021-10-13T02:09:10+00:00 1 Answer 0

Answers ( )

    0
    2021-10-13T02:10:22+00:00

    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

    #LearnwithBrainly

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