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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Grade 7 - Mathematics
8.2 Problems on Quadrilaterals - I

  1. Example:

  2. In a quadrilateral, three angles are 55, 65 and 105 , Find the fourth angle?

    Solution: (Ist Method)
    We know that
    The sum of the four angles of a quadrilateral is 360.
    The sum of the given three angles = 55 + 65+ 105 = 225
    The fourth angle = 360 - 225 = 135.

  3. Example:
    The two angles of a quadrilateral are equal with degree measure 76 and the third angle is given as 120. Find the fourth angle.

    Solution: (IInd method)
    The sum of the angles of a quadrilateral = 360.
    Let 'x' be then fourth angle.
    Therefore 76 + 76 + 120 + x = 360: (Since two of its angles are of 76).
    That is 272 + x = 360:
    Therefore x = 360 - 272 = 88.
    Hence the fourth angle is 88.

  4. Example:
    In a quadrilateral, the third angle is 2 times the fourth and the second angle is 3 times the fourth. The first angle is given as 120. Find the fourth angle.

    Solution:
    Let the fourth angle be 'x'.
    Here, the third angle = 2 times the fourth angle = 2x.
    The second angle = 3 times the fourth angle = 3x.
    We know the sum of the angles of a quadrilateral = 360.
    Therefore x + 2x + 3x + 120 = 360.
    ie 6x + 120 = 360.
    ie 6x = 360 - 120 = 240.
    ie x = 240 / 6 = 40.
    Hence the fourth angle = 40.


Directions: Read the above example carefully and answer the following questions:
  1. The sum of the first two angles of a quadrilateral is given by 204. Also given that the third angle is 3 times the fourth. Find the third and fourth angles.
  2. In a quadrilateral, the third angle is 2 times the fourth and the second angle is 3 times the fourth. The first angle is given as 120. Find the fourth angle.

Q 1: The sum of the first two angles of a quadrilateral is given by 200. Find the sum of the remaining angles.
160
60
200

Q 2: If, in a quadrilateral, three angles are 90, 90 and 100, then find its fourth angle.
40
80
90

Q 3: In a quadrilateral, the sum of two angles are given by 120 and one of the angle is 100, then the fourth angle is
140
90
220

Q 4: In a quadrilateral, three angles are 50, 90 and 90. The fourth angle will be ________.
140
160
130

Question 5: This question is available to subscribers only!

Question 6: This question is available to subscribers only!


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