Question

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

Answer 1

Hint: To find the measure of the angles we make use of the relation, opposite angles in the parallelogram are equal and the sum of all the angles in a parallelogram is 360°.

Complete step-by-step answer:
We know, opposite angles in the parallelogram are equal.
Let one of the angles be x°.

Given Data – Sum of two opposite angles of a parallelogram is 130°.
$
   \Rightarrow {\text{2x = 130}}^\circ \\
   \Rightarrow {\text{x = }}\dfrac{{130^\circ }}{2} \\
   \Rightarrow {\text{x = 65}}^\circ \\
$

We know that the sum of all the angles in a parallelogram is 360°.

Now, let the two other opposite angles be a°.

⟹130° + 2a = 360°
⟹2a = 230°
⟹a = 115°

So, two angles in the parallelogram are 65° and the other two angles are 115°.

Note: In order to solve this type of questions the key is to consider one of the unknown, opposite angles as x, and perform the appropriate operations in order to determine its angle. Then we consider the other angle as a, use the obtained value of x and determine its angle as well. Having enough knowledge in concepts of parallelogram is essential.