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

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But it need to be listed that the two angles that room supplementary to each other, perform not need to be beside each other. Hence, any type of two angles can be supplementary angles, if their amount is same to 180°.

Geometry is among the essential branches of math that deals with the study of different shapes. That initiates the research of lines and angles. A directly line is a line without curves and also it is defined as the shortest distance in between two points. An edge is created when the line segment meets at a point.

## What space Supplementary Angles?

In Maths, the definition of supplementary is pertained to angles the make a directly angle together. The means, two angles are said to it is in supplementary angles when they include up come 180 degrees. Two angles room supplementary, if

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

This way that ∠A + ∠B = 180°.

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

Some that the instances of supplementary angle are:

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

## Properties of Supplementary Angles

The vital properties that supplementary angles are:

The 2 angles are stated to be supplementary angles once they add up to 180°.The two angles with each other make a directly line, but the angles require not it is in together.“S” that supplementary angles represents the “Straight” line. This way they type 180°.

There are two varieties of supplementary angles:

The supplementary angles that have actually a typical arm and also a typical vertex room called nearby supplementary angles. The surrounding supplementary angles share the usual line segment and vertex through each other.

For example, the supplementary angles 110° and 70°, in the offered figure, are adjacent to each other. The supplementary angle that carry out not have actually a common arm and also a common vertex are dubbed non-adjacent supplementary angles. The non-adjacent supplementary angles execute not share the heat segment or vertex v each other.

For example, the supplementary angles 130° and 50°, in the provided figure, space non-adjacent to each other. ## How to uncover Supplementary Angles?

As us know, if the sum of 2 angles is equal to 180°, climate they room supplementary angles. Every of the angle is stated to be a complement of one more angle. Hence, we can determine the complement of an angle, by subtracting it from 180°.

For example, if friend had given that 2 angles that form supplementary angles. If one edge is ∠A then an additional angle ∠B is the supplement. Hence,

∠A = 180° – ∠B (or)

∠B = 180° – ∠A

## Supplementary angle Theorem

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

Proof:

If ∠x and ∠y room two different angles that are supplementary to a third angle ∠z, such that,

∠x + ∠z = 180 ……. (1)

∠y + ∠z = 180 ……. (2)

Then, indigenous the above two equations, we can say,

∠x = ∠y

Hence proved.

## Supplementary and Complementary Angles

Both supplementary and also complementary angles room pairs that angles, that amount up come 180° and also 90°, respectively. Let united state find an ext differences between the pair that angles.

 Complementary Angles Supplementary Angles Sum of two 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 linked together. Supplementary angles type a straight line. The complement of an edge A is (90 – A)° The supplement of an edge A is (180 – A)°

## Problems and also Solutions top top Supplementary angles

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

We know 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 also ∠y are supplementary angles and ∠x = 67, then uncover ∠y.

Solution: Given, ∠x and also ∠y are supplementary angles

And

∠x = 67°

Since, ∠x + ∠y = 180°

∠y = 180 – ∠x

∠y = 180 – 67

∠y = 113°

### Practice Questions

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

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No, two acute angle cannot kind a supplementary angle.By definition, acute angles are the angles that measure up the angle better than 0° and also less than 90°. If you add two acute angles in which each angle is large as possible, its amount will be much less than 180°. By the an interpretation of supplementary angles, it is difficult to obtain the supplementary angle once we add two acute angles.Example: 80° +60° = 140° which is no a supplementary angle.But, in the case, if us add more than 2 acute angles, we can acquire supplementary angles.
No, 2 obtuse angles cannot type a supplementary angle.By the definition of obtuse angles, the angle that measure better than 90° are obtuse. If you add two obtuse angles, the sum will be greater than 180°. It will not fulfill the property of the supplementary angles when we include obtuse angles.Example: 110° + 95° = 205° i beg your pardon is not a supplementary angle. <205° > 180° >
Yes, 2 ideal angles can form a supplementary angle. We recognize that when the measure of an edge is specifically 90°, climate it is known as a best angle.When two appropriate angles are added, that is feasible to obtain the supplementary angle. Because 90° + 90° = 180°, together it satisfies the problem of supplementary angles.

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