There are four interior angles in a parallelogram and the sum of the interior angles of a parallelogram is always 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. Show
Properties of Angles of a ParallelogramA 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:
Theorems Related to Angles of a ParallelogramThe 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:
Let us learn about these two special theorems of a parallelogram in detail. Opposite Angles of a Parallelogram are EqualTheorem: 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: 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. Consecutive Angles of a Parallelogram are SupplementaryThe consecutive angles of a parallelogram are supplementary. Let us prove this property considering the following given fact and using the same figure. Given: ABCD is a parallelogram, with four angles ∠A, ∠B, ∠C, ∠D respectively. Related Articles on Angles of a ParallelogramCheck out the interesting articles given below that are related to the angles of a parallelogram.
FAQs on Angles of a ParallelogramDo 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°. 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. In this case, a parallelogram consists of 2 triangles, so, the sum of the interior angles is 360°. This can also be calculated by the formula, S = (n − 2) × 180°, where 'n' represents the number of sides in the polygon. Here, 'n' = 4. Therefore, the sum of the interior angles of a parallelogram = S = (4 − 2) × 180° = (4 − 2) × 180° = 2 × 180° = 360°. What is the Relationship Between the Adjacent Angles of a Parallelogram?The adjacent angles of a parallelogram are also known as consecutive angles and they are always supplementary (180°). How are the Opposite Angles of a Parallelogram Related?The opposite angles of a parallelogram are always equal, whereas, the adjacent angles of a parallelogram are always supplementary. How to Find the Missing Angles of a Parallelogram?We can easily find the missing angles of a parallelogram with the help of three special properties:
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. What is the Sum of the Interior Angles of a Parallelogram?The sum of the interior angles of a parallelogram is always 360°. According to the angle sum property of polygons, the sum of the interior angles of a polygon can be found by the formula, S = (n − 2) × 180°, where 'n' shows the number of sides in the polygon. In this case, 'n' = 4. Therefore, the sum of the interior angles of a parallelogram = S = (4 − 2) × 180° = (4 − 2) × 180° = 2 × 180° = 360°. Are the Angles of a Parallelogram 90 Degrees?In some parallelograms like rectangles and squares, all the angles measure 90°. However, the angles in the other parallelograms may not necessarily be 90°. Are the Opposite Angles of a Parallelogram Congruent?Yes, the opposite angles of a parallelogram are congruent. However, the adjacent angles of a parallelogram are always supplementary. Are Consecutive Angles of a Parallelogram Congruent?No, the consecutive (adjacent) angles of a parallelogram are not congruent, they are supplementary. Are the Opposite Angles of a Parallelogram Supplementary?No, according to the theorems based on the angles of a parallelogram, the opposite angles are not supplementary, they are equal. How do you find the measurement 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. Here, 'n' = 4. Therefore, the sum of the interior angles of a parallelogram = S = (4 − 2) × 180° = (4 − 2) × 180° = 2 × 180° = 360°.
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