# 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.

Video Solution
Practical Geometry
Ex 10.4 | Question 3

## 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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