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Question

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

(a) 108

(b) 54

(c) 72

(d) 81


Solution

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∘

Mathematics
Secondary School Mathematics IX
Standard IX

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