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

## 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 \(ΔDEF.\)