# Excercise 6.2 The-Triangle-and-its-Properties- NCERT Solutions Class 7

Go back to  'The Triangle and its Properties'

## Chapter 6 Ex.6.2 Question 1

Find the value of the unknown exterior angle $$x$$ in the following diagrams:

### Solution

What is known:

Measurement of interior opposite angles.

What is unknown:

Value of the unknown exterior angle $$x$$.

Reasoning:

We know that an exterior angle of a triangle is the sum of interior opposite angles. By using this fact, we can find out the unknown exterior angle $$x.$$

Steps:

(i) Interior angles are $$50^\circ$$ and $$70^\circ$$

\begin{align} \text{Exterior angle}=&\left[ \begin{array} \, \text{Sum of interior} \\ \text{opposite angles} \\ \end{array} \right] \\ x=&50^\circ + 70^\circ \\ x=&120^\circ \end{align}

(ii) Interior angles are $$65^\circ$$ and $$45^\circ$$

\begin{align} \text{Exterior angle}=&\left[ \begin{array} \, \text{Sum of interior} \\ \text{opposite angles} \\ \end{array} \right] \\ x=&65^\circ + 45^\circ \\ x=&110^\circ \end{align}

(iii) Interior angles are $$30^\circ$$ and $$70^\circ$$

\begin{align} \text{Exterior angle}=&\left[ \begin{array} \, \text{Sum of interior} \\ \text{opposite angles} \\ \end{array} \right] \\ x=&30^\circ + 70^\circ \\ x=&100^\circ \end{align}

(iv) Interior angles are $$60^\circ$$ and $$60^\circ$$

\begin{align} \text{Exterior angle}=&\left[ \begin{array} \, \text{Sum of interior} \\ \text{opposite angles} \\ \end{array} \right] \\ x=&60^\circ + 60^\circ \\ x=&120^\circ \end{align}

(v) Interior angles are $$50^\circ$$ and $$50^\circ$$

\begin{align} \text{Exterior angle}=&\left[ \begin{array} \, \text{Sum of interior} \\ \text{opposite angles} \\ \end{array} \right] \\ x=&50^\circ + 50^\circ \\ x=&100^\circ \end{align}

(vi) Interior angles are $$30^\circ$$ and $$60^\circ$$

\begin{align} \text{Exterior angle}=&\left[ \begin{array} \, \text{Sum of interior} \\ \text{opposite angles} \\ \end{array} \right] \\ x=&30^\circ + 60^\circ \\ x=&90^\circ \end{align}

## Chapter 6 Ex.6.2 Question 2

Find the value of the unknown interior angle $$x$$ in the following figures:

### Solution

What is known?

One of the interior opposite angle and exterior angle.

What is unknown?

interior opposite angle $$x$$.

Reasoning:

We know that the sum of interior opposite angle is equal to the exterior angle. By using this fact, we can find the unknown interior angle.

Steps:

(i) Exterior angle is $$115^\circ$$

\begin{align} \text{Exterior angle}=&\left[ \begin{array} \, \text{Sum of interior} \\ \text{opposite angles} \\ \end{array} \right] \\ 115^\circ =&x+ 50^\circ \\x=&115^\circ- 50^\circ \\ x=&65^\circ \end{align}

(ii) Exterior angle is $$100^\circ$$

\begin{align} \text{Exterior angle}=&\left[ \begin{array} \, \text{Sum of interior} \\ \text{opposite angles} \\ \end{array} \right] \\ 100^\circ =&x+ 70^\circ \\x=&100^\circ- 70^\circ \\ x=&30^\circ \end{align}

(iii) Exterior angle is $$125^\circ$$

\begin{align} \text{Exterior angle}=&\left[ \begin{array} \, \text{Sum of interior} \\ \text{opposite angles} \\ \end{array} \right] \\ 125^\circ =&x+ 90^\circ (90^\circ \rm{given})\\x=&125^\circ- 90^\circ \\ x=&35^\circ \end{align}

(iv) Exterior angle is $$120^\circ$$

\begin{align} \text{Exterior angle}=&\left[ \begin{array} \, \text{Sum of interior} \\ \text{opposite angles} \\ \end{array} \right] \\ 120^\circ =&x+ 60^\circ \\x=&120^\circ- 60^\circ\\ x=&60^\circ \end{align}

(v) Exterior angle is $$80^\circ$$

\begin{align} \text{Exterior angle}=&\left[ \begin{array} \, \text{Sum of interior} \\ \text{opposite angles} \\ \end{array} \right] \\ 80^\circ =&x+ 30^\circ \\x=&80^\circ- 30^\circ \\ x=&50^\circ \end{align}

(vi) Exterior angle is $$75^\circ$$

\begin{align} \text{Exterior angle}=&\left[ \begin{array} \, \text{Sum of interior} \\ \text{opposite angles} \\ \end{array} \right] \\ 75^\circ =&x+ 35^\circ \\x=&75^\circ- 35^\circ \\ x=&40^\circ \end{align}