Question

the ratio between the adjacent angels of parallelogram is 2:3 respectively half the smaller angle of the parallelogram is equal to the smallest angle of quadrilateral largest angle of quadrilateral is four times its smallest angle. what is the sum of largest angle of quadrilateral and the smaller angle of parallelogram ​

Answer 1

Let the adjacent angles of parallelogram be 2x∘and 3x∘ respectively

then 2x∘+3x∘ = 180∘

=> 5x∘ = 180∘ => x∘=36∘

Smaller angle of parallelogram = 2x = 72∘

= Smallest angle of the quadrilateral = 36∘

Therefore, Its largest angle = 4×36=144∘

Therefore, Required sum = 144 + 72 = 216∘