Question

# If opposite angles of a parallelogram are supplementary, then the parallelogram is _____ .

A
Trapezium
B
Rectangle
C
Rhombus
D
None of the above

Solution

## The correct option is B RectangleWe know that, the opposite angles of a parallelogram are equal. ie. ∠ A=∠ C and ∠ B=∠ D ...(i) If they are supplementary as well, then ∠ A+∠ C=180∘  from (i), ∠ A+∠ A=180∘  2∠ A=180∘  ∠ A=90∘  Similarly, ∠ C=90∘  It means that each angle will be equal to 90∘. A parallelogram whose internal angles are all 90∘ is a rectangle. Thus, the figure will be a rectangle. Mathematics

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