Grade 8 Questions on Angles with Solutions and Explanations

Detailed solutions and full explanations to grade 8 math questions on angles are presented.

Find the unknown angles in the figures below.

  1. angle problems 1

    .
    Solution
    The sum of all 3 interior angles of a triangle is equal to 180. Hence
    92 + 27 + x = 180
    Solve for x
    x = 180 - (92 + 27) = 61

  2. angle problems 2

    .
    Solution
    The sum of all 3 interior angles of the right triangle is equal to 180. Hence
    y + 34 + 90 = 180
    Solve for y
    y = 180 - (90 + 34) = 56

  3. angle problems 3

    .
    Solution
    Angle y and angle of measure 56 are supplementary. Hence
    y + 56 = 180
    Solve for y
    y = 180 - 56 = 124
    Angle x and angle of measure 144 are supplementary. Hence
    x + 144 = 180
    Solve for x
    x = 180 - 144 = 36
    The sum of angles x, y and z of the triangle is equal to 180
    x + y + z = 180
    Substitute x and y by their values found above.
    36 + 124 + z = 180
    Solve for z.
    z = 20

  4. angle problems 4

    .
    Solution
    Let z be the third angle of the triangle on the right. The sum of the interior angles in the triangle on the right side is equal to 180. Hence
    26 + 26 + z = 180 z = 180 - 26 - 26 = 128
    Angles z and y are supplementary. Hence
    z + y = 180
    Solve for y
    y = 180 - z = 180 - 128 = 52
    The sum of the interior angles in the angle on the left is equal to 180. Hence
    x + y + 64 = 180
    Solve for x
    x = 180 - 64 - 52 = 64

  5. angle problems 5

    .
    Solution
    Angle z and the angle of measure 133 are supplementary angles. Hence
    z + 133 = 180
    z = 180 - 133 = 47
    The angles of the lower triangle add up to 180. Hence
    33 + 133 + x = 180
    x = 180 - 33 - 133 = 14
    The sum of the measures of the angles of the upper triangle is equal to 180. Hence
    y + z + 114 = 180
    y = 180 - 114 - Z , z = 47 found before
    y = 180 - 114 - 47 = 19

  6. angle problems 6

    .
    Solution
    The sum of the angles of the triangle on the right side is equal to 180. Hence
    w + 131 + 32 = 180
    w = 180 - 131 - 32 = 17
    Angle v and the angle with measure 132 are supplementary. Hence
    132 + v = 180
    v = 180 - 132 = 48
    The three angles of the triangle in the middle add up to 180. Hence
    v + z + 122 = 180
    z = 180 - 122 - v
    z = 180 - 122 - 48 = 10 , v = 48 found above
    Angle x and the angle with measure 122 are supplementary. Hence
    x + 122 = 180
    x = 180 - 122 = 58
    The three angles of the triangle on the left side add up to 180. Hence
    x + 43 + y = 180
    y = 180 - 43 - x
    y = 180 - 43 - 58 = 79 , x = 58 found above.

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Updated: 22 July 2018 (A Dendane)