Ex.6.2 Q2 The Triangle and Its Properties - NCERT Maths Class 7

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Question

Find the value of the unknown interior angle \(x\) in the following figures:

Text 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 \(75^\circ\)

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

  
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