Question

the sum of two opposite angles of a parallelogram is 130°. Find all the angles of the parallelogram

Answer 1

Hey there !

Solution :

We know that Sum of Opposite angles of a Parallelogram = 130°

We know that Opposite sides of a Parallelogram are equal.

Hence let the angles of the Parallelogram be ∠ A , ∠ B , ∠ C , ∠ D.

Given that, ∠ A + ∠ C = 130°

Since  ∠ A = ∠ C , we can write it as :

2 ∠ A = 130°

=> ∠ A = 130 / 2 = 65°

We also know that, Adjacent angles in a parallelogram are supplementary. Hence we get,

=> ∠ A + ∠ B = 180°

=> 65° + ∠ B = 180°

=> ∠ B = 180° - 65°

=> ∠ B = 115°

We know that, ∠ B = ∠ D ( Opposite angles )

Hence all the angle measures are : 65°, 115°, 65°, 115°.

Hope my answer helped !

Answer 2

A quadrilateral in which both pairs of opposite sides are parallel is called a parallelogram.

The properties of parallelogram are :
➡A parallelogram has four vertices.
➡A parallelogram has four sides.
➡A parallelogram has two diagonals.
➡The sum of all the four angles of a parallelogram is 360°.

Q. The sum of two opposite angles of a parallelogram is 130°. Find all the angles of the parallelogram.

Solution :

All the angles of parallelogram are,
∠A , ∠B , ∠C , ∠D

Given that :-
∠A + ∠C = 130°

As one of the property of the parallelogram says that opposite angles of a parallelogram are equal.

So,
∠A = ∠C

We can write
=> 2∠A = 130°
=> ∠A = 130°/2
=> ∠A = 65°

Now,
∠A = 65° , ∠C = 65°

Now,

∠B =  ∠D 

We know that sum of all angles of parallelogram (quadrilateral) = 360°.

=> ∠A +  ∠C+ ∠B + ∠D = 360°

(∠A + ∠C) = 130°

=> 130° + ∠B + ∠D = 360°

=> ∠B + ∠D = 360° - 130°

=> ∠B + ∠D = 230°

as,

∠B + ∠D = 230°

we can write,
=> 2∠B = 230°
=> ∠B = 230°/2
=> ∠B = 115°

So,
∠B = 115° , ∠D = 115°

Hence all the angles of parallelogram are :

∠A= 65°
 ∠B = 115° 
∠C = 65°
 ∠D = 115°