Question

The sum of two opposite angles of a parallelogram is 130°. Find the measure of each of its angles.

Answer 1

Let ABCD is a parallelogram. 

∠ B + ∠ D = 130° 

∠B + ∠B = 130° (Opposite angles of parallelogram are equal) 

∠B = 65° 

∠D = 65° 

Now, ∠B + ∠C = 180° (sum of any two adjacent angles of a parallelogram is 180°) 

∠C = 180° - ∠B = 115° 

Now, ∠A = ∠C = 115° (Opposite angles of parallelogram are equal) 

Therefore, ∠A = 115°, ∠B = 65°, ∠C = 115° and ∠D = 65°.