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20 March, 14:40

Given that the quadrilateral shown is a parallelogram. Use the properties of parallelograms to find x if ∠A = 133° and ∠D = (3x + 35) °. A) x = 2 B) x = 4 C) x = 5 D) x = 7 2) Use the properties of parallelograms to find x if ∠A = 122° and ∠C = (2x + 60) °. A) x = 27 B) x = 29 C) x = 31 D) x = 33

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  1. 20 March, 14:43
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    (i) Option B, x=4

    (ii) Option C, x=31

    Step-by-step explanation:

    Step 1:

    Angle properties of parallelogram is as follows:

    - Opposite angles are equal

    - Adjacent angles are supplementary, i. e the sum of the adjacent angles are 180

    Step 2:

    ∠A and ∠D are adjacent and hence their sum is equal to 180

    So, 133 + 3 x + 35 = 180

    => 3 x + 168 = 180

    => 3 x = 180-168 = 12

    => x = 4

    Step 3:

    ∠A and ∠C are opposite and hence they are equal

    So, 2 x + 60 = 122

    2 x = 62

    x = 31
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