Question

Which kind of triangle CANNOT be constructed?

A. an isosceles triangle with an obtuse angle
B. an equilateral triangle with an acute angle
C. a scalene triangle with an acute angle
D. a right triangle with an obtuse angle

Answer 1

Answer: D. a right triangle with an obtuse angle

Reason:

For any triangle the 3 inside angles always add to 180 degrees.

A right triangle has exactly one angle that is 90 degrees (aka a right angle). Meanwhile, an obtuse triangle has exactly one angle that is over 90 degrees. An example would be something like 105 degrees.

A triangle with both a right angle and obtuse angle is impossible. Note how 90+105 = 195 isn't 180. It being well over means that there's no room for the third angle to fit in.