Question

The sum of opposite angles of a parallelogram is 100◦. Find all the angles of the parallelogram.​

Answer 1

ABCD is a parallelogram.

∠B+∠D=130∘

∠B=∠D (opposite angles of a parallelogram are equal) 

∠B=∠B=130∘

2∠B=130∘ 

b = {130}{2}

∠B=65∘

Now ∠B+∠C=180∘ (adjacent angles of a parallelogram are supplementary )

∠C=180∘−∠B=180∘−65∘ 

∠C=115∘

∴∠A=∠C=115∘ (opp. angles of parallelogram are equal) 

∴∠B=∠D=65∘ and ∠A=∠C=115∘