Question

A student is asked to draw a triangle whose angles are 90°, 90° and 20°. Which of the following is possible with the given measures?

• A. He can draw a right angled triangle.
• B. He can draw an equilateral triangle.
• C. He cannot draw any triangle.
• D. He can draw an obtuse angled triangle.

Answer 1

The correct option is C

He cannot draw any triangle.

Explanation for the correct option:

Option (C) He cannot draw any triangle.

Here according to the question

Sum of all angles =$90°+90°+20°=200°$.

But according to the analysis of geometry

We know that, Sum of all angles of the triangle =$180°$.

But here we have$200°$, which is not possible.

So we cannot draw any triangle using this measurement.
Explanation for the incorrect option:

Option (A) He can draw a right angled triangle.

In a right angle triangle, one angle is 90° and the other is less than 90°.

So, by using this concept, the given option is incorrect.

Hence, option A is incorrect.

Option (B)He can draw an equilateral triangle.

As we know that

By definition of an equilateral triangle, each angle of an equilateral triangle is 60°

But, here two angles is 90 degree, and one is 20°

So, option B is incorrect.

Option (D) He can draw an obtuse angled triangle.

In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

But here this is not possible.

Hence, option D is incorrect.

Hence, option C is correct.