Question

If an angle of a parallelogram is two thirds of its adjacent angle, the smallest angle of the parallelogram is

(a) ${108}^{\circ }$

(b) ${54}^{\circ }$

(c) ${72}^{\circ }$

(d) ${81}^{\circ }$

Answer 1

Let the adjacent angles be x
then , other angle = (2/3)x

we know opposite angles of parallelogram are equal .

=> and sum of all angles of a quadrilateral is 360°

therefore ,
we get ,

=> x+x+2x/3+2x/3 = 360°
=> 2x+4x/3 = 360°

=> (6x+4x)/3 = 360° (making denominator equal)

=> 10x/3 = 360°

=> x = 360×3/10
=> x = 36×3 = 108°


therefore , other angle = (2/3)x
=> (2/3)×108°

=> 2×36 => 72°



therefore , smallest angle of Parallelogram is 72°


(c) 72∘