Ex.10.4 Q3 Practical Geometry Solution- NCERT Maths Class 7

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Question

Examine whether you can construct \(ΔDEF\) such that \(EF = 7.2\,\rm{ cm},\) \(m∠E = 110^\circ\) and \(m∠F = 80^\circ. \)Justify your answer.

Text Solution

 

What is known?

Length of one side of a triangle and measure of two angles.

What is unknown?

Whether a triangle be constructed with the given values of length and angles.

Reasoning:

By using the angle sum property, we can find out the third angle. If the angle sum property is followed, then it is possible to construct a triangle and if not then we cannot construct a triangle.

Steps:

We will use angle-sum property of a triangle to find the measure of \(∠D\)

By angle sum property,

\(∠E +∠F + ∠D =\) \(180^\circ .\)

\(110^\circ + 80^\circ + ∠D =\) \(180^\circ. \)

\(190^\circ + ∠D\) \(=\) \(180^\circ .\)

So, \(∠D = -10^\circ\)

Angle of \(-10^\circ\) is not possible, thus we cannot construct triangle \(ΔDEF.\)

  
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