Examine whether you can construct ∆DEF such that EF = 7.2 cm, m∠E = 110° and m∠F = 80°. Justify your answer

Solution:

For the given triangle we can find the third angle by using the angle sum property of a triangle 

If the angle sum property is satisfied, then it is possible to construct the triangle ∆DEF such that EF = 7.2 cm, m∠E = 110°, and m∠F = 80°, and if not then we cannot construct a triangle.

By angle sum property of a triangle,

∠E + ∠F + ∠D = 180°

110° + 80° + ∠D = 180°

So, ∠D = -10°

The angle −10° is not possible as it is negative, thus we cannot construct triangle ΔDEF.

☛ Check: NCERT Solutions for Class 7 Maths Chapter 10

Video Solution:

Examine whether you can construct ∆DEF such that EF = 7.2 cm, m∠E = 110° and m∠F = 80°. Justify your answer.

Class 7 Maths NCERT Solutions Chapter 10 Exercise 10.4 Question 3

Summary:

We have examined if ∆DEF can be constructed or not such that EF = 7.2 cm, m∠E = 110°, and m∠F = 80°. We get −10° as the third angle which is not possible, thus we cannot construct triangle ΔDEF.

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