Multiple Choice Question (MCQ)

The angles of a quadrilateral ABCD taken in an order are in the ratio 3 : 7 : 6 : 4. Then ABCD is a

  1. ×

    kite

  2. ×

    parallelogram

  3. ×

    rhombus

  4. trapezium

Collected in the board: Quadrilateral

Steven Zheng posted 2 days ago

Answer

  1. Given, the angles of a quadrilateral ABCD taken in an order are in the ratio 3:7:6:4

    We have to find the type of the quadrilateral.

    Let the angles of the quadrilateral ABCD be 3x, 7x, 6x and 4x.

    We know that the sum of all angles of a quadrilateral is equal to 360 degrees.

    Therefore

    3x + 7x + 6x + 4x = 360°

    20x = 360°

    x = \dfrac{360°}{20}

    x = 18°

    Now four interior angles are calculated below

    A = 3x = 3\cdot 18° = 54°

    B = 7x = 7\cdot 18° = 126°

    C = 6x = 6\cdot 18° = 108°

    D = 4x = 4\cdot 18° = 72°

    AD and BC are two lines cut by a transversal CD.

    Now, sum of angles C and D on the same side of transversal,

    C + D =108° + 72° =180°

    This is the same for angle A and B

    A + B =54° + 126° =180°

    We know that the sum of interior angles on the same side of the transversal is equal to 180 \degree , then the two lines are parallel.

    therefoer, AD|| BC

    This implies ABCD is a quadrilateral in which one pair of opposite sides are parallel.

    Therefore, ABCD is a trapezium.

Steven Zheng posted 2 days ago

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