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18 April, 18:59

When parallel lines are cut by a transversal, why are same-side interior angles supplementary? Use the fact that a line parallel to the transversal can be drawn to form a parallelogram in your answer.

A because the sum of the measures of a pair of same-side interior angles is equal to one-fourth the number of degrees in a parallelogram

B because the sum of the measures of a pair of same-side interior angles is equal to one-half the number of degrees in a parallelogram

C because the sum of the measures of a pair of same-side interior angles is equal to the number of degrees in a parallelogram

D because the sum of the measures of a pair of same-side interior angles is equal to twice the number of degrees in a parallelogram

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Answers (1)
  1. 18 April, 20:46
    0
    Because the sum of the measures of a pair of same-side interior angles

    is equal to one-half the number of degrees in a parallelogram ⇒ B

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - In a parallelogram every two opposite sides are parallel

    - In a parallelogram every tow opposite angles are equal

    ∵ The parallelogram is a quadrilateral

    ∵ The sum of the measures of the interior angles in any quadrilateral

    is 360°

    ∵ In parallelogram each two opposite angles are equal

    ∴ The sum of the measures of every two adjacent angles

    equal 360° : 2 = 180°

    * Lets solve the problem

    - When parallel lines are cut by a transversal

    ∵ It is a fact that the parallel lines and their transversal can form a

    parallelogram

    ∵ The sum of the measures of the adjacent angles of the

    parallelogram is 180°

    ∵ The sum of the measures of the supplementary angles is 180°

    ∴ The same side-interior angles are supplementary, because

    they are two adjacent angles in a parallelogram

    * Lets find the true statement

    ∵ The sum of the measures of every two adjacent interior angles

    in the parallelogram = 360° : 2 = 180°

    ∵ 180° is half the sum of the measures of interior angles in the

    parallelogram

    ∴ Because the sum of the measures of a pair of same-side interior

    angles is equal to one-half the number of degrees in a

    parallelogram
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