Which Angle is Supplementary to Lsm

Supplementary angles and complementary angles
are defined with respect to the improver of ii angles. If the sum of two angles is 180 degrees and so they are said to exist supplementary angles, which class a linear angle together. Whereas if the sum of two angles is 90 degrees, then they are said to be complementary angles, and they form a right angle together.

When 2 line segments or lines meet at a common signal (called a vertex), at the indicate of intersection an bending is formed. When a ray is rotated about its endpoint, and so the mensurate of its rotation in an anti-clockwise direction is the bending formed between its initial and final position.

In fig. 1 if the ray OP is rotated in the direction of the ray OQ, so the measure of its rotation represents the angle formed by information technology. In this example, the measure of rotation which is the angle formed between the initial side and the final side is represented by Ɵ.

Complementary Angles

When the sum of two angles is 90°, then the angles are known as
complementary angles. In other words, if two angles add upwards to form a correct angle, then these angles are referred to as complementary angles. Here we say that the two angles complement each other.

How to Observe Complementary Angles?

Suppose if i angle is 10 then the other angle will be 90° – x. Hence, we apply these complementary angles for trigonometry ratios, where one ratio is complementary to another ratio past 90 degrees such every bit;

• sin (90° – A) = cos A and cos (90° – A) = sin A
• tan (90° – A) = cot A and cot (90° – A) = tan A
• sec (ninety° – A) = cosec A and cosec (90° – A) = sec A

Hence, you tin encounter here the trigonometric ratio of the angles gets changed if they complement each other.

In the above figure, the measure of bending BOD is sixty
^°

and bending AOD measures xxx
^°
. By adding both of these angles we get a right angle, therefore ∠BOD and ∠AOD are complementary angles.

The post-obit angles in Fig. 3 given below are complementary to each other as the measure of the sum of both the angles is ninety
^°
. ∠POQ and ∠ABC are complementary and are called
complements
of each other.

For case:


To detect the complement of 2x + 52°, subtract the given angle from 90 degrees.

90^o

 –  (2x + 52^o

) =  90^o

 – 2x – 52^o

  = -2x + 38^o

The complement of 2x + 52^o
is 38^o

 – 2x.

Supplementary Angles

When the sum of two angles is 180°, then the angles are known as supplementary angles. In other words, if two angles add up, to class a straight angle, and then those angles are referred to as
supplementary angles.

How to Discover Supplementary Angles?

The ii angles form a linear angle, such that, if 1 angle is 10, then the other the angle is 180°
– x. The linearity hither proves that the properties of the angles remain the same. Take the examples of trigonometric ratios such as;

• Sin (180 – A) = Sin A
• Cos (180 – A) = – Cos A (quadrant is changed)
• Tan (180 – A) = – Tan A

In Fig. 4 given higher up, the measure of ∠AOC is 60^o
and ∠AOB measures 120^o. Past adding both of these angles we get a straight angle. Therefore, ∠AOC and ∠AOB are supplementary angles, and both of these angles are known as a supplement to each other.

Also, acquire:

• Side by side Angles Vertical
• Lines And Angles

Difference betwixt Complementary and Supplementary Angles

How to remember easily the departure between Complementary angles and supplementary angles?

• “C“ letter of the alphabet ofComplementary stands for “Corner” (A right angle,90
  
  
  
  ^°
  
  
  )
• “S“letter ofSupplementary stands for “Straight” ( a directly line,
  180
  ^°
  
  )

Video Lesson on Types of Angles

Solved Examples

The case problems on supplementary and complementary angles are given beneath:

Example 1:

Find the complement of 40 degrees.

Solution:

Equally the given angle is twoscore degrees, and then,

The complement is 50 degrees.

We know that sum of complementary angles =  ninety degrees

And then, 40°
 + 50°
 = 90°

Example two:

Find the supplement of the angle 1/3 of 210°.

Solution:

Pace 1:

Catechumen i/3 of 210°

That is, (1/three) ten 210° = 70°

Step 2:

Supplement of 70° = 180° – 70° = 110°

Therefore, the supplement of the bending 1/3 of 210° is 110°

Example three:

The measures of the 2 angles are (x + 25)° and (3x + 15)°. Find the value of 10 if angles are supplementary angles.

Solution:

Nosotros know that,

Sum of Supplementary angles =  180 degrees

Then,

(10 + 25)° + (3x + 15)° = 180°

4x + twoscore°
  = 180°

4x = 140°

x = 35°

The value of x is 35 degrees.

Example 4:

The divergence between the 2 complementary angles is 52°. Find both the angles.

Solution:

Let, Outset angle = m degrees, and so,

Second angle =  (ninety – m)degrees   {as per the definition of complementary angles}

Difference between angles = 52°

Now,

 (ninety° – g) – m = 52°

90° – 2m = 52°

 – 2m = 52° – ninety°

-2m = -38°

m = 38°/2°

m = xix°

Again, 2nd angle = 90° – xix°
  = 71°

Therefore, the required angles are 19°, 71°.

Practise Questions

1. Check if 65° and 35° are complementary angles.
2. Are 80° and 100° supplementary?
3. Find the complement of 54°.
4. Notice the supplement of 99°.
5. If one angle measures 50° and is supplementary to another angle. And so discover the value of another angle. Also, state what type of angle it is?