# Ex.6.2 Q1 The Triangle and Its Properties - NCERT Maths Class 7

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## Question

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

## Text 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}

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