Question

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

Answer 1

As we know that the opposite angles of a parallelogram are equal,

So, let the measure of each angle be x°.

Their sum = 130°

According to condition,

x+x = 130

or, 2x = 130

or, x = 130/2

or, x = 65

So, the angles are of 65°.

And the sum of two adjacent angles of a parallelogram is 180°.

So, let the angle adjacent to 65° be x°.

According to condition,

x+65 = 180

or, x = 180-65

or, x = 115

So, the angle is 115°.

Hence, the angles of each of its angles are 65°, 115°, 65° and 115°.