![]() What is the Sum of the Interior Angles of a Parallelogram? 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. No, all the angles of a parallelogram are not equal. The interior angles of a parallelogram sum up to 360° and any two adjacent (consecutive) angles of a parallelogram are supplementary. The angles made on the inside of a parallelogram and formed by each pair of adjacent sides are its interior angles. What are the Interior Angles of a Parallelogram? The sum of all the angles of a parallelogram is equal to 360°.The consecutive angles of a parallelogram are supplementary.The opposite angles of a parallelogram are congruent.We can easily find the missing angles of a parallelogram with the help of three special properties: How to Find the Missing Angles of a Parallelogram? The opposite angles of a parallelogram are always equal, whereas, the adjacent angles of a parallelogram are always supplementary. How are the Opposite Angles of a Parallelogram Related? The adjacent angles of a parallelogram are also known as consecutive angles and they are always supplementary (180°). What is the Relationship Between the Adjacent Angles of a Parallelogram? This can also be calculated by the formula, S = (n − 2) × 180°, where 'n' represents the number of sides in the polygon. In this case, a parallelogram consists of 2 triangles, so, the sum of the interior angles is 360°. According to the angle sum property of polygons, the sum of the interior angles in a polygon can be calculated with the help of the number of triangles that can be formed inside it. For example, in a parallelogram ABCD, ∠A + ∠B + ∠C + ∠D = 360°. Yes, all the interior angles of a parallelogram add up to 360°. Related Articles on Angles of a ParallelogramĬheck out the interesting articles given below that are related to the angles of a parallelogram.įAQs on Angles of a Parallelogram Do Angles in a Parallelogram add up to 360°? ![]() Hence, it is proved that the consecutive angles of a parallelogram are supplementary. Therefore, the sum of the respective two adjacent angles of a parallelogram is equal to 180°. ![]() Proof: If AD is considered to be a transversal and AB || CD.Īccording to the property of transversal, we know that the interior angles on the same side of a transversal are supplementary. ![]() Given: ABCD is a parallelogram, with four angles ∠A, ∠B, ∠C, ∠D respectively. Let us prove this property considering the following given fact and using the same figure. The consecutive angles of a parallelogram are supplementary. Consecutive Angles of a Parallelogram are Supplementary This shows that the consecutive angles are supplementary. = 2(∠A + ∠B) = 360º (We can substitute ∠C with ∠A and ∠D with ∠B since it is given that ∠A =∠C and ∠B =∠D) The sum of all the four angles of this quadrilateral is equal to 360°. Given: ∠A =∠C and ∠B=∠D in the quadrilateral ABCD. The converse of the above theorem says if the opposite angles of a quadrilateral are equal, then it is a parallelogram. Hence proved, that opposite angles in any parallelogram are equal. This gives ∠B = ∠D by CPCT (corresponding parts of congruent triangles). Thus, the two triangles are congruent, △ABC ≅ △ADC Proof: In the parallelogram ABCD, diagonal AC is dividing the parallelogram into two triangles. Theorem: In a parallelogram, the opposite angles are equal. Opposite Angles of a Parallelogram are Equal Let us learn about these two special theorems of a parallelogram in detail.
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