Angle

**Category : **7th Class

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

**Answer:** (c)

**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

**Answer:** (d)

**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

**Answer:** (c)

**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

**Answer:** (b)

**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

**Answer:** (d)

**Adjacent Angles **

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.

*play_arrow*Introduction*play_arrow*Some Terms Related to Lines*play_arrow*Angle*play_arrow*Parallel Lines*play_arrow*Lines & Angles

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