# 7th Class Mathematics Lines and Angles Angle

## Angle

Category : 7th Class

### Angle

If two rays have common end point then the inclination between two rays is called angle. In the figure O is the vertex, $\overline{OP}$ and $\overline{OQ}$ are called arm of the angle. It is represented by notation$\angle$.

Types of angle

Acute Angle

Tangle whose measure is more than $0{}^\circ$ and less than $90{}^\circ .$

Right Angle

The angle of measure $90{}^\circ$

Obtuse Angle

The angle whose measure is more than 90° and less than $180{}^\circ .$

Straight Angle

The angle whose measure is $180{}^\circ$

Reflex Angle

The angle whose measure is more than $180{}^\circ$and less than $360{}^\circ .$

Complete Angle

The angle whose measure is 360°.

Equal Angles

Two angles are said to be equal if they are of same measure.

Complementary Angles

If the sum of measure of two angles is ${{90}^{o}}$ then they are said to be complementary angles .e.g $75{}^\circ$ and $15{}^\circ$ are complementary angles and they are said to be complement of each other.

Supplementary Angles

If the sum of measure of two angles is $180{}^\circ$then they are said to be supplementary angles, e.g $107{}^\circ$ and $73{}^\circ$ are said to be supplement of each other.

Which one of the following statements is not true?

(i) A line segment has finite length

(ii) A line has only one dimension

(iii) A line $\overleftrightarrow{AB}$ and $\overleftrightarrow{BA}$represents the same

(iv) A ray $\overleftrightarrow{AB}$and $\overleftrightarrow{BA}$represents the same

(a) i, ii

(b) ii and iii

(c) Only iv

(d) iii and iv

(e) None of these

Explanation

and are different rays. They are started from different end points A and B respectively.

Therefore, option (c) is correct and rest of the options is incorrect.

In the following AD is the bisector of $\angle EAF$

Which one of the following statements is incorrect?

(a) $\angle EAD$is an acute angle

(b) $\angle BAE$is an obtuse angle

(c)$\angle FAD$ and $\angle DAE$are complement to each other

(d) $\angle CAD$and $\angle DAE$are not complement to each other

(e) None of these

Explanation

Since $\angle EAD=\angle CAD=45$degree hence, option (a) is correct.

$\angle BAE$is more than 90° therefore, it is obtuse hence, option (b) is also correct.

The sum of $\angle FAD$and $\angle DAE$is $90{}^\circ$ hence, option (c) is also correct

$\left( \angle CADand\text{ }\angle DAE \right)$and $\left( \angle FAD\text{ }and\text{ }\angle DAE \right)$are the same. Therefore, they are also complement.

If the difference of two supplementary angles is $50{}^\circ$ then find the measurement of the smaller angle.

(a) 67°

(b) $75{}^\circ$

(c)$~65{}^\circ$

(d) $90{}^\circ$

(e) None of these

Explanation

Let the one angle be x then other angle will be $180{}^\circ -x.$

By given condition$~x-(180{}^\circ -x)=50{}^\circ$

$2x=180{}^\circ +50{}^\circ \Rightarrow 2x=230{}^\circ \text{ }\Rightarrow x=115{}^\circ$

Hence, the measurement of smaller angle $=\text{ }180{}^\circ -115{}^\circ =65{}^\circ$

Find the supplement of an angle which is 8 times of its complement.

(a) 90°

(b) 100°

(c) 80°

(d) 70°

(e) None of these

If the angle and its complement are x and $\sqrt{x}$ respectively then find the angle.

(a)$11{}^\circ ,\text{ }12{}^\circ$

(b) $13{}^\circ ,\text{ }14{}^\circ$

(c)$-15{}^\circ ,1{}^\circ$

(d) $81{}^\circ$

(e) None of these

Two angles are said to be adjacent angles, if

• They have a common vertex
• They have common arm and
• Non-common arms are opposite to the common arm.

In the given figure $\angle POQ,\text{ }\angle QOR$ are adjacent angles

Linear Pair of Angles

If the sum of measure of two adjacent angles is $180{}^\circ$ then they are said to be linear pair of angles. In the linear pair non-common arms are opposite to each other.

In the figure $\angle ROS$and $\angle TOS$are linear pairs.

Vertically Opposite Angles

It is the pair of angle which is formed by two intersecting lines having no common arms. In the given figure $\angle AOC$and $\angle BOD$are vertically opposite angles. Similarly $\angle AOD$and $\angle BOC$are also vertically opposite angles.

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