Supplementary angles are those angles that sum up to 180 degrees. For example, edge 130° and also angle 50° room supplementary angles since sum that 130° and also 50° is same to 180°. Similarly, safety angles include up come 90 degrees. The 2 supplementary angles, if joined together, type a directly line and also a straight angle.

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But it have to be listed that the 2 angles that room supplementary to each other, execute not have to be next to each other. Hence, any type of two angles can be supplementary angles, if their amount is equal to 180°.

Geometry is among the vital branches of mathematics that faces the study of various shapes. The initiates the research of lines and angles. A directly line is a line without curves and it is defined as the shortest distance in between two points. An edge is formed when the heat segment meets at a point.


Table of contents:Definition

What room Supplementary Angles?

In Maths, the an interpretation of supplementary is related to angles the make a right angle together. That means, two angles are stated to be supplementary angle when they add up to 180 degrees. Two angles room supplementary, if

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

This way that ∠A + ∠B = 180°.

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

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Examples that 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 crucial properties of supplementary angles are:

The 2 angles are stated to it is in supplementary angles as soon as they add up come 180°.The 2 angles with each other make a right line, but the angles need not it is in together.“S” the supplementary angles stands for the “Straight” line. This means they kind 180°.

Adjacent and Non-Adjacent Supplementary Angles

There space two types of supplementary angles:

Adjacent supplementary anglesNon-adjacent supplementary angles

Adjacent Supplementary angles

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

For example, the supplementary angles 110° and 70°, in the given figure, are surrounding to each other.

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Non-adjacent Supplementary angles

The supplementary angles that carry out not have actually a common arm and a usual vertex are referred to as non-adjacent supplementary angles. The non-adjacent supplementary angles execute not re-publishing the line segment or vertex with each other.

For example, the supplementary angles 130° and 50°, in the offered figure, are non-adjacent to every other.

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How to find Supplementary Angles?

As we know, if the amount of two angles is same to 180°, climate they space supplementary angles. Each of the angles is said to it is in a supplement of an additional angle. Hence, we can determine the complement of an angle, by subtracting it indigenous 180°.

For example, if you had provided that 2 angles that form supplementary angles. If one angle is ∠A then another angle ∠B is that is supplement. Hence,

∠A = 180° – ∠B (or)

∠B = 180° – ∠A

Supplementary angles Theorem

The supplementary edge theorem says that if two angles are supplementary come the exact same angle, climate the 2 angles are said to be congruent.

Proof:

If ∠x and also ∠y space two various angles that are supplementary come a third angle ∠z, together that,

∠x + ∠z = 180 ……. (1)

∠y + ∠z = 180 ……. (2)

Then, indigenous the above two equations, we deserve to say,

∠x = ∠y

Hence proved.

Supplementary and also Complementary Angles

Both supplementary and complementary angles room pairs of angles, that amount up to 180° and also 90°, respectively. Let united state find much more differences in between the pair of angles.


Complementary AnglesSupplementary Angles
Sum of 2 angles is 90°Sum of 2 angles is 180°
Ex: ∠A + ∠B = 90°.Ex: ∠A + ∠B = 180°.
Complementary angles kind a right-angled triangle when an unified together.Supplementary angles kind a right line.
The complement of an edge A is (90 – A)°The supplement of an angle A is (180 – A)°

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Problems and also Solutions ~ above Supplementary angles

Question 1: Find the measure of one unknown angle from the provided figure.

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Solution:

We recognize that the supplementary angles add up come 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 room 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 edge 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 are the angles that measure the angle better than 0° and also less 보다 90°. If you add two acute angles in which each angle is large as possible, its amount will be much less than 180°. Through the definition of supplementary angles, the is difficult to acquire the supplementary angle once we add two acute angles.Example: 80° +60° = 140° which is not a supplementary angle.But, in the case, if us add more than 2 acute angles, us can gain supplementary angles.
No, 2 obtuse angle cannot form a supplementary angle.By the an interpretation of obtuse angles, the angles that measure higher than 90° space obtuse. If you include two obtuse angles, the sum will be higher than 180°. It will not meet the building of the supplementary angles as soon as we add obtuse angles.Example: 110° + 95° = 205° i m sorry is no a supplementary angle. <205° > 180° >
Yes, 2 best angles can kind a supplementary angle. We recognize that once the measure of an angle is specifically 90°, then it is known as a ideal angle.When two ideal angles space added, that is feasible to gain the supplementary angle. Because 90° + 90° = 180°, as it satisfies the problem of supplementary angles.

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Supplementary and complementary both are various angles. Supplementary add upto 180 degrees whereas security angles add to 90 degrees.