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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