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Lines and Angles

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7th class > Lines and Angles > Related Angles

Related Angles

Now, let's talk about when two or more angles are bunched together. Such angles are called angles.

Use the mouse to move the point around and observe the range of the angle measures that fall under the given categories

Based on the sum of measures of two adjacent angles we have:

If the sum of the measures of two angles is 90°, the angles are called angles.

Whenever two angles are complementary, each angle is said to be the complement of the other angle.

For eg: in the below diagram, the ‘35° angle’ is the complement of the ‘65° angle’ and vice versa.

Below, ∠POR and ∠ROQ measures will always add upto ° i.e. complementary angles.

Think and Answer

Instruction

Can two obtuse angles be complementary?
No, as an obtuse angle has a measure greater than 90° while a pair of complementary angles have a sum equalling 90°.
Can two acute angles be complementary?
Yes, as acute angles have a measure less than 90° and two such angles can together have a sum angle measure of 90°.
Can two right angles be complementary?
No, since two right angles (each having a measure of 90°) which form a supplementary angle i.e. 180°.

1. Which pairs of following angles are complementary?

Solution:

Two angles are called complementary when their measures add to 90 degrees.

Instruction

Instruction

2. What is the measure of the complement of each of the following angles? (i) 45º (ii) 65º (iii) 41º (iv) 54º
Solution: The complement of an angle is the amount you need to add to it to make 90°.
Let's find the complement for each given angle:
(i) 45°: Complement = 90 - 45 = °
(ii) 65°: Complement = 90- 65 = °
(iii) 41°: Complement = 90 - 41 = °
(iv) 54°: Complement = 90 - 54 = °
So, the complements are: (i) 45° (ii) 25° (iii) 49° (iv) 36°

3. The difference in the measures of two complementary angles is 12°. Find the measures of the angles.

Solution:

Step 1: Solve for x

Since, x and y are complementary angles: x + y = ° (1)

Given: x − y = 12° (2)

Adding the two equations of (1) and (2):

(x+y) + (x−y) = 90° + 12° ⟹ = °

⟹ x = °

Step 2: Solve for y:

Substitute x = 51° back into the first equation (1):

51° + y = 90° ⟹ y = 90° − 51° ⟹ y = °

Therefore, the measures of the two complementary angles are 51° and 39°.

When the sum of the measures of the angles is 180º, such pairs of angles are called angles.

When two angles are supplementary, each angle is said to be the supplement of the other. See the below image: ‘80° angle’ is the supplement of the ‘100° angle’ and vice versa.

Below, ∠AOC and ∠COB measures will always add upto ° i.e. supplementary angles.

Think and Answer

Instruction

Can two obtuse angles be supplementary?
No, as obtuse angles are always larger than 90° and the sum will therefore, result on an angle measure greater than 180°.
Can two acute angles be supplementary?
No, as the acute angles will have a measure less than 90° and together the two angles will have a angle sum probably greater than 90° but definitely less than 180°.
Can two right angles be supplementary?
Yes, since two right angles (each having a measure of 90°) upon adding, will give an angle measure of 180°.

Instruction

The difference in the measures of two complementary angles is 12°. Find the measures of the angles. ° , ° (Enter in increasing order of measure)
Let one of the complementary angle be a. Then, the complement to angle a will be (90° - a).

From the question we know, (90° - a) - a = 12°

Upon, solving we get , 90° - 2a = °

Therefore, a = 39° and the complement angle (90° - a) = 51°
  • What is the measure of the complement of each of the following angles?

Instruction

Classify the below given pairs of angles as Complementary / Supplementary / Neither of the options:

Instruction

1.Find the pairs of supplementary angles below figures?

Solution:

Two angles are called supplementary when their measures add up to 180 degrees.

Instruction

Instruction

2. What will be the measure of the supplement of each one of the following angles? (i) 100º (ii) 90º (iii) 55º (iv) 125º

(i) For 100°: º − º = º
So, the supplement of 100º is 80º.
(ii) For 90º: º − º = º
So, the supplement of 90º is 90º.
(iii) For 55º: 180º − 55º = º
So, the supplement of 55º is 125º.
(iv) For 125º: 180º − 125º = º
So, the supplement of 125º is 55º.

3. Among two supplementary angles the measure of the larger angle is 44º more than the measure of the smaller. Find their measures.

Solution:

Let the measure of the smaller angle be x degrees.

Since the angles are supplementary, their sum is °.

We can write the measure of the larger angle be x + 44°.

Setting up the equation for the sum of the two angles:

x + (x + 44) = °

Simplify and solve for x :

2x + = 180

2x = 180 - 44 =

2x = 136 ⟹ x = °

So, the measure of the smaller angle is 68°.

Find the measure of the larger angle:

x + 44 = 68° + 44° = °

So, the measure of the larger angle is 112°.

Therefore, the measures of the two supplementary angles are:

Smaller angle: °

Larger angle: °