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: 9 April 2009 (A Dendane)
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