Supplementary angles are those angle that amount up to 180 degrees. For example, angle 130° and angle 50° space supplementary angles because sum the 130° and 50° is same to 180°. Similarly, safety angles add up come 90 degrees. The two supplementary angles, if join together, type a straight line and a right angle.

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But it need to be noted that the 2 angles that room supplementary to each other, do not have to be beside each other. Hence, any two angles deserve to be supplementary angles, if their sum is equal to 180°.

Geometry is among the vital branches of mathematics that encounters the research of different shapes. The initiates the research of lines and angles. A directly line is a line without curves and also it is defined as the shortest distance between two points. An angle is developed when the line segment meets at a point.


Table the contents:Definition

What room Supplementary Angles?

In Maths, the meaning of supplementary is concerned angles that make a right angle together. It means, two angles are said to it is in supplementary angle when they include up come 180 degrees. 2 angles room supplementary, if

One of its angles is an acute angle and also another angle is one obtuse angle.Both that the angle are right angles.

This means that ∠A + ∠B = 180°.

See the figure listed below for a much better understanding of the pair of angle that space supplementary.

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Examples the Supplementary Angles

Some of the examples of supplementary angle are:

120° + 60° = 180°90° + 90° = 180°140° + 40° = 180°96° + 84° = 180°

Properties the Supplementary Angles

The essential properties the supplementary angle are:

The 2 angles are claimed to it is in supplementary angles when they add up come 180°.The two angles with each other make a straight line, however the angles require not be together.“S” the supplementary angles means the “Straight” line. This means they form 180°.

Adjacent and also Non-Adjacent Supplementary Angles

There space two species of supplementary angles:

Adjacent supplementary anglesNon-adjacent supplementary angles

Adjacent Supplementary angles

The supplementary angle that have a typical arm and a typical vertex space called adjacent supplementary angles. The nearby supplementary angle share the common line segment and also vertex v each other.

For example, the supplementary angle 110° and 70°, in the offered figure, are nearby to every other.

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Non-adjacent Supplementary angles

The supplementary angles that do not have a typical arm and a common vertex are referred to as non-adjacent supplementary angles. The non-adjacent supplementary angles carry out not re-superstructure the heat segment or vertex with each other.

For example, the supplementary angle 130° and 50°, in the given figure, space non-adjacent to every other.

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How to uncover Supplementary Angles?

As we know, if the amount of two angles is equal to 180°, climate they are supplementary angles. Every of the angle is claimed to it is in a supplement of an additional angle. Hence, we can determine the supplement of one angle, by individually it indigenous 180°.

For example, if friend had offered that two angles that kind supplementary angles. If one angle is ∠A then another angle ∠B is its supplement. Hence,

∠A = 180° – ∠B (or)

∠B = 180° – ∠A

Supplementary angles Theorem

The supplementary angle theorem states that if two angles space supplementary come the same angle, climate the 2 angles are claimed to it is in congruent.

Proof:

If ∠x and also ∠y room two different angles that space supplementary come a 3rd angle ∠z, together that,

∠x + ∠z = 180 ……. (1)

∠y + ∠z = 180 ……. (2)

Then, indigenous the above two equations, we have the right to say,

∠x = ∠y

Hence proved.

Supplementary and Complementary Angles

Both supplementary and also complementary angles room pairs the angles, that amount up come 180° and 90°, respectively. Let us find more differences between the pair of angles.


Complementary AnglesSupplementary Angles
Sum of 2 angles is 90°Sum of two angles is 180°
Ex: ∠A + ∠B = 90°.Ex: ∠A + ∠B = 180°.
Complementary angles type a right-angled triangle when merged together.Supplementary angles form a straight line.
The enhance of an angle A is (90 – A)°The complement of an angle A is (180 – A)°

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Problems and Solutions on Supplementary angles

Question 1: Find the measure up of an unknown edge from the offered figure.

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Solution:

We recognize that the supplementary angles add up to 180°.

X + 55° + 40° = 180°

X + 95° = 180°

X = 180°- 95°

X = 85°

Therefore, the unknown angle, X = 85°

Question.2: If ∠x and ∠y space supplementary angles and also ∠x = 67, then discover ∠y.

Solution: Given, ∠x and ∠y space supplementary angles

And 

∠x = 67°

Since, ∠x + ∠y = 180°

∠y = 180 – ∠x 

∠y = 180 – 67

∠y = 113°

Practice Questions

What is the supplement of angle 65 degrees?Are the angle 80° and also 120° supplementary?Find the complement of 140°.

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No, two acute angles cannot kind a supplementary angle.By definition, acute angles room the angles that measure the angle better than 0° and less than 90°. If you add two acute angles in which every angle is big as possible, its sum will be less than 180°. By the definition of supplementary angles, the is impossible to gain the supplementary angle once we add two acute angles.Example: 80° +60° = 140° i m sorry is not a supplementary angle.But, in the case, if we add much more than two acute angles, us can acquire supplementary angles.
No, 2 obtuse angles cannot kind a supplementary angle.By the an interpretation of obtuse angles, the angles that measure better than 90° are obtuse. If you include two obtuse angles, the amount will be higher than 180°. It will certainly not meet the residential property of the supplementary angles once we include obtuse angles.Example: 110° + 95° = 205° which is not a supplementary angle. <205° > 180° >
Yes, 2 ideal angles can kind a supplementary angle. We recognize that as soon as the measure up of an edge is exactly 90°, climate it is well-known as a appropriate angle.When two best angles room added, it is possible to obtain the supplementary angle. Since 90° + 90° = 180°, together it satisfies the problem of supplementary angles.

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Supplementary and also complementary both are various angles. Supplementary include upto 180 degrees whereas safety angles add to 90 degrees.