Angles of a Parallelogram
There are four interior angles in a parallelogram and the sum of the angles of a parallelogram sum up to 360°. The opposite angles of a parallelogram are equal and the consecutive angles of a parallelogram are supplementary. Let us read more about the properties of the angles of a parallelogram in detail.
Properties of Angles of a Parallelogram
A parallelogram is a quadrilateral with equal and parallel opposite sides. There are some special properties of a parallelogram that make it different from the other quadrilaterals. Observe the following parallelogram to relate to its properties given below:
 The opposite angles of a parallelogram are congruent (equal). Here, ∠A = ∠C; ∠D = ∠B.
 All the angles of a parallelogram add up to 360°. Here,∠A + ∠B + ∠C + ∠D = 360°.
 All the respective consecutive angles are supplementary. Here, ∠A + ∠B = 180°; ∠B + ∠C = 180°; ∠C + ∠D = 180°; ∠D + ∠A = 180°
Theorems Related to Angles of a Parallelogram
The theorems related to the angles of a parallelogram are helpful to solve the problems related to a parallelogram. Two of the important theorems are given below:
 The opposite angles of a parallelogram are equal.
 Consecutive angles of a parallelogram are supplementary.
Let us learn about these two special theorems of a parallelogram in detail.
Opposite Angles of a Parallelogram are Equal
Theorem: In a parallelogram, the opposite angles are equal.
Given: ABCD is a parallelogram, with four angles ∠A, ∠B, ∠C, ∠D respectively.
To Prove: ∠A =∠C and ∠B=∠D
Proof: In the parallelogram ABCD, diagonal AC is dividing the parallelogram into two triangles. On comparing triangles ABC, and ADC. Here we have:
AC = AC (common sides)
∠1 = ∠4 (alternate interior angles)
∠2 = ∠3 (alternate interior angles).
Thus, the two triangles are congruent, △ABC ≅ △ADC
This gives ∠B = ∠D by CPCT (corresponding parts of congruent triangles).
Similarly, we can show that ∠A =∠C.
Hence proved, that opposite angles in any parallelogram are equal.
The converse of the above theorem says if the opposite angles of a quadrilateral are equal, then it is a parallelogram. Let us prove the same.
Given: ∠A =∠C and ∠B=∠D in the quadrilateral ABCD.
To Prove: ABCD is a parallelogram.
Proof:
The sum of all the four angles of this quadrilateral is equal to 360°.
= [∠A + ∠B + ∠C + ∠D = 360º]
= 2(∠A + ∠B) = 360º (since it is given that ∠A =∠C and ∠B=∠D)
= ∠A + ∠B = 180º which shows that the consecutive angles are supplementary.
This must mean that AD  BC. Similarly, we can show that AB  CD.
Hence, AD  BC, and AB  CD.
Therefore ABCD is a parallelogram.
Consecutive Angles of a Parallelogram Are Supplementary
The consecutive angles of a parallelogram are supplementary. Let us prove this property considering the following given fact and using the figure given above.
Given: ABCD is a parallelogram, with four angles ∠A, ∠B, ∠C, ∠D respectively.
To prove: ∠A + ∠B = 180°, ∠C + ∠D = 180°.
Proof: If AD is considered to be a transversal and AB  CD.
According to the property of transversal, we know that interior angles on the same side of a transversal are supplementary.
Therefore, ∠A + ∠D = 180°.
Similarly,
∠B + ∠C = 180°
∠C + ∠D = 180°
∠A + ∠B = 180°
Therefore, the sum of the respective two adjacent angles of a parallelogram is equal to 180°.
Hence, it is proved that the consecutive angles of a parallelogram are supplementary.
Related Articles on Angles of a Parallelogram
Check out the interesting articles given below that are related to the angles of a parallelogram.
Solved Examples on Angles of a Parallelogram

Example 1: One angle of a parallelogram measures 75°. Find the measure of its adjacent angle and the measure of all the remaining angles of the parallelogram.
Solution :
Given that one angle of a parallelogram = 75°
Let the adjacent angle be x
We know that the consecutive (adjacent) angles of a parallelogram are supplementary.
Therefore, 75° + x° = 180°
x = 180°  75° = 105°
To find the measure of all the four angles of a parallelogram we know that the opposite angles of a parallelogram are congruent.
Hence, ∠1 = 75°, ∠2 = 105°, ∠3 = 75°, ∠4 = 105° 
Example 2: The values of the opposite angles of a parallelogram are given as follows: ∠1 = 75°, ∠3 = (x + 30)°, find the value of x.
Given: ∠1 and ∠3 are opposite angles of a parallelogram.Solution:
Given: ∠1 = 75° and ∠3 = (x + 30)°
We know that the opposite angles of a parallelogram are congruent.
Therefore,
(x + 30)° = 75°
x = 75°  30°
x = 45°
Hence, the value of x is 45°.
FAQs on Angles of a Parallelogram
Do Angles in a Parallelogram Add Up to 360?
Yes, all the interior angles of a parallelogram add up to 360°. For example, in a parallelogram ABCD, ∠A + ∠B + ∠C + ∠D = 360°.
How do You Find the Angles of a Parallelogram?
We can easily find angles of a parallelogram with the help of three special properties:
 The opposite angles of a parallelogram are congruent.
 The consecutive angles of a parallelogram are supplementary.
 The sum of all the angles of a parallelogram is equal to 360°.
What are the Interior Angles of a Parallelogram?
The angles made on the inside of a parallelogram and formed by each pair of adjacent sides are its interior angles. The interior angles of a parallelogram sum up to 360° and any two adjacent (consecutive) angles of a parallelogram are supplementary.
Are all Angles in a Parallelogram Equal?
No, all the angles of a parallelogram are not equal. There are two basic theorems related to the angles of a parallelogram which state that the opposite angles of a parallelogram are equal and the consecutive (adjacent) angles are supplementary.
Are the Angles of a Parallelogram 90 Degrees?
Geometric shapes like rectangles and squares follow the basic property of parallelograms which states that opposite sides and angles are congruent. These are some special cases in which all the angles of a parallelogram measure 90 degrees, as in the case of a square and a rectangle.
Are Opposite Angles Supplementary?
No, according to the theorems based on the angles of a parallelogram, the opposite angles are not supplementary, they are equal.