Question

Examine whether you can construct ΔDEF such that EF = 7.2 cm, m∠E =

110° and m∠F = 80°. Justify your answer.

Answer 1

Given that,

m∠E = 110° and m∠F = 80°

Therefore,

m∠E + m∠F = 110° + 80° = 190°

However, according to the angle sum property of triangles, we should obtain

m∠E + m∠F + m∠D = 180°

Therefore, the angle sum property is not followed by the given triangle. And thus, we cannot construct ΔDEF with the given measurements.

Also, it can be observed that point D should lie on both rays, EX and FY, for constructing the required triangle. However, both rays are not intersecting each other. Therefore, the required triangle cannot be formed.