Examine whether you can construct ΔDEF such that EF = 7.2 cm, m ∠E = 110^o and m ∠F = 80^o. Justify your answer.

Question

Examine whether you can construct &#x394;DEF such that EF = 7.2 cm, m &#x2220; E = 110 o and m &#x2220; F = 80 o . Justify your answer.

Philoid · Accepted Answer

Here,

According to the question,

It is given that,

∠E = 110° and ∠F = 80°

That shows that ∠E + ∠F = 110 + 80

= 190°

This is greater than 180°

And, we know that,

The sum of interior angles of triangle is 180°

Hence,

The given measurements cannot form a triangle.

We have to draw figure using following steps of construction:

Step 1: Draw a line segment EF of 7.2 cm

Step 2: Now, from point E draw a ray EX making an angle of 110° from EF.

Step 3: From F, draw a ray FY from EF making 80° angle

Now, we can observe that EX and FY does not intersect.

Hence,

The ΔDEF is not possible.

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