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# Lines and Angles Worksheet

Lines and Angles Worksheet help students to study different figures in which corners are formed when two or more lines or line segments meet at a point. Here, we can observe various types of lines and angles. Thus, studying lines and angles concepts thoroughly will help deal with such figures and understand how to use them efficiently.

Learn: Lines and Angles

Lines and angles worksheets for class 7 and 9 students are excellent sources who wish to develop and enhance their skills in angles. These worksheets have concepts such as identifying the names of angles, lines, classifying lines and angles, measuring angles and other exciting concepts.

Benefits of Practicing Lines and Angles Worksheet

Lines and angles worksheets help the students understand lines and lines along with their classification in a better way. Students can try solving these lines and angles worksheets to assess themselves in basic geometry concepts, namely lines, angles and their applications. Students of class 7 and class 9 will find these maths worksheets helpful for their board exams preparation.

Students can download the Lines and Angles class 7 worksheet and Lines and Angles class 9 worksheet given below. These worksheets will help them in practising questions and excel in their problem solving skills.

 Lines and Angles Worksheet Class 7 Lines and Angles Worksheet Class 9

## Examples On Lines And Angles

Example 1:

Find the complements of the angles given below.

a] 20°

b] 60°

c] 5°

d] 17°

Solution:

The complements of the angles are

a] 20° is 70°.

b] 60° is 30°.

c] 5° is 85°.

d] 17° is 73°.

Example 2:

Find the supplements of the angles given below.

a] 9°

b] 30°

c] 135°

d] 178°

Solution:

The supplements of the angles are

a] 9° is 171°.

b] 30° is 150°.

c] 135° is 45°.

d] 178° is 2°.

Example 3:

Find a pair of complementary angles such that one angle is 1/2 of another angle.

Solution:

If one angle is ½ of another angle, then one of the angles is 30° and the other angle is 60°.

Example 4:

The measure of an angle is 4 times the measure of its supplement. Find the angles.

Solution:

Let “x” be an angle.

Given that the measure of an angle is 4 times the measure of its supplement.

(i.e) If the measure of one angle is “x”, then the measurement of the supplementary angle will be (180° -x).

Therefore,

⟹ x = 4(180° -x)

⟹  x = 4(180°) – 4x

⟹ x+4x = 720°

⟹ 5x = 720°

⟹x = 720/5 = 144°.

Therefore, the measurement of supplementary angles = 180° – 144° = 36°.

Hence, the angles are 36° and 144°.

Example 5:

A, B and C are the three angles of a triangle. If A − B = 15° and B − C = 30°, find ∠A, ∠B and∠C.

Solution:

Given that:

A-B = 15° …(1)

B-C = 30° …(2)

We know that sum of angles of a triangle is 180°.

(i.e) A+B+C = 180° …(3)

By using the equation (1) and (2), equation (3) can be written as follows:

(B+15°) + B + (B-30°) = 180°

3B -15° = 180°

3B = 180° + 15°

3B = 195°

B = 195°/3 = 65°.

Hence, B = 65°.

Now, substitute B = 65° in (1)

(i.e) A – 65° = 15°

A = 15°+65° = 80°

Similarly, substitute B = 65° in (2), we get

65° – C = 30°

C = 65° – 30°

C = 35°

Hence, the angles are: ∠A = 80°, ∠B =65° and ∠C = 35°.

Example 6:

In a ΔABC, if 2∠A = 3∠B = 6∠C, find the measures of∠A, ∠B and ∠C.

Solution:

Let us assume the angle be x

Therefore, ∠A = x/2, ∠B = x/3 and ∠C = x/6

We know that the sum of interior angles of a triangle is 180°.

(i.e) (x/2) + (x/3) + (x/6) = 180°

12x/12 = 180°

x = 180°.

Hence, ∠A = x/2 = 180/2 = 90°

∠B = x/3 = 180/3 = 60°

∠C = x/6 = 180/6 = 30°

Hence, the angles are ∠A = 90°, ∠B =60° and ∠C = 30°.

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