Answer:
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
