There are four interior angle in a parallelogram and also the sum of the internal angles that a parallel is always 360°. The opposite angles of a parallelogram space equal and the consecutive angles of a parallelogram space supplementary. Let united state read more about the properties of the angles of a parallel in detail.

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1.Properties of angles of a Parallelogram
2.Theorems pertained to Angles of a Parallelogram
3.FAQs on angle of a Parallelogram

A parallelogram is a quadrilateral through equal and parallel opposite sides. There room some special properties that a parallelogram that make it various from the other quadrilaterals. Watch the complying with parallelogram to relate come its properties offered below:

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All the angles of a parallelogram add up come 360°. Here,∠A + ∠B + ∠C + ∠D = 360°.All the corresponding consecutive angles room supplementary. Here, ∠A + ∠B = 180°; ∠B + ∠C = 180°; ∠C + ∠D = 180°; ∠D + ∠A = 180°

Theorems concerned Angles the a Parallelogram


The theorems pertained to the angles of a parallel are valuable to fix the difficulties related come a parallelogram. 2 of the important theorems are offered below:

The opposite angle of a parallelogram room equal.Consecutive angles of a parallelogram space supplementary.

Let us learn around these 2 special theorems that a parallel in detail.

Opposite angle of a Parallelogram space Equal

Theorem: In a parallelogram, the contrary 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 line AC is separating the parallelogram right into two triangles. ~ above comparing triangle ABC, and also ADC. Below we have:AC = AC (common sides)∠1 = ∠4 (alternate inner angles)∠2 = ∠3 (alternate inner angles)Thus, the 2 triangles room congruent, △ABC ≅ △ADCThis offers ∠B = ∠D by CPCT (corresponding components of congruent triangles).Similarly, we can show that ∠A =∠C.Hence proved, the opposite angles in any kind of parallelogram space equal.

The converse of the over theorem claims if the opposite angle of a quadrilateral are equal, then it is a parallelogram. Let us prove the same.

Given: ∠A =∠C and also ∠B=∠D in the quadrilateral ABCD.To Prove: ABCD is a parallelogram.Proof:The amount of all the four angles the this square is same to 360°.= <∠A + ∠B + ∠C + ∠D = 360º>= 2(∠A + ∠B) = 360º (We deserve to substitute ∠C v ∠A and also ∠D v ∠B since it is offered that ∠A =∠C and also ∠B =∠D)= ∠A + ∠B = 180º . This shows that the continuous angles space supplementary. Hence, it method that ad || BC. Similarly, us can present that ab || CD.Hence, advertisement || BC, and abdominal || CD.Therefore ABCD is a parallelogram.

Consecutive angle of a Parallelogram room Supplementary

The consecutive angles of a parallelogram are supplementary. Let united state prove this residential property considering the adhering to given fact and using the exact same figure.

Given: ABCD is a parallelogram, with 4 angles ∠A, ∠B, ∠C, ∠D respectively.To prove: ∠A + ∠B = 180°, ∠C + ∠D = 180°.Proof: If advertisement is considered to be a transversal and abdominal || CD.According to the property of transversal, we understand that the interior angles ~ above the same side the a transversal room supplementary.Therefore, ∠A + ∠D = 180°.Similarly,∠B + ∠C = 180°∠C + ∠D = 180°∠A + ∠B = 180°Therefore, the amount of the particular two nearby angles that a parallelogram is same to 180°.Hence, the is proved that the consecutive angles of a parallelogram room supplementary.

Related short articles on angles of a Parallelogram

Check out the interesting articles given below that are regarded the angle of a parallelogram.


Example 1: One angle of a parallelogram actions 75°. Discover the measure up of its nearby angle and the measure of every the remaining angles of the parallelogram.

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Solution:

Given the one angle of a parallel = 75°Let the surrounding angle it is in xWe know that the continually (adjacent) angle of a parallelogram room supplementary.Therefore, 75° + x° = 180°x = 180° - 75° = 105°To discover the measure of every the four angles the a parallel we recognize that the opposite angle of a parallelogram space congruent.Hence, ∠1 = 75°, ∠2 = 105°, ∠3 = 75°, ∠4 = 105°


Example 2: The worths of the opposite angle of a parallelogram are given as follows: ∠1 = 75°, ∠3 = (x + 30)°, find the value of x.Given: ∠1 and ∠3 are opposite angle of a parallelogram.

Solution:

Given: ∠1 = 75° and ∠3 = (x + 30)°We know that the opposite angles of a parallelogram space equal.Therefore,(x + 30)° = 75°x = 75° - 30°x = 45°Hence, the value of x is 45°.