which set of angles can form a triangle

Question:- which set of angles can form a triangle

A. 2 acute and 1 right

B. 1 acute and 2 obtuse

C. 1 acute and 2 right

D. 1 acute, 1 right, and 1 obtuse

Answer: D. 1 acute, 1 right, and 1 obtuse

To create a triangle out of any three angles, their sum should total to180 degrees. A triangle can have the following combinations of angles:

A. 2 acute angles (less than 90 degrees) and one right angle measuring 90 degree. Since the sum of these numbers is less than 180 degrees, this cannot be a triangle.

B. One angle is acute and two are obsolete (greater than 90 degrees). Since the sum will be greater than 180 degrees, it cannot construct a triangle.

C. 1 acute angle and two right angles makes almost 270 degree which is above 180 degrees, which means no triangle can be formed from the sum of angles.

D) An acute angle, a right angle and an obtuse. So this combination can form a triangle because their sums add up to 180 degrees.

In brief, the only possible angles combination from provided options to guarantee triangle angle sum property is D option consisting of 1 acute and two more obtuse angels. The sums of the other options are either less or more than 180 degrees, which contradicts with triangle angle-sum property. Thus, set D is the correct angles that can form a triangle.