Q. 34.3( 35 Votes )

Two adjacent angles of a parallelogram are in the ratio 4 : 5. Find the measure of each of its angles.

Answer :

Let x be the common multiple.


Since the sum of any two adjacent angles of a parallelogram is 180°,


A + B = 180°


4x + 5x = 180°


9x = 180°


x = 20°


A = 80°


B = 100°


Also, B + C = 180° [Since, B and C are adjacent angles]


100° + C = 180°


C = (180° - 100°) = 80°


Further, C + D = 180° [Since, C and D are adjacent angles]


80° + D = 180°


D = (180° - 80°) = 100°


Therefore, A = 80°, B = 100°, C = 80° and D = 100°.


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