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 1

A: 2 acute and 1 right

Explanation:

A triangle is a polygon that has 3 sides as well as three angles

Triangles can be can be classified based on their three sides as well as their three angles.

Based on their sides, we have 3 types of triangles.

1. Equilateral triangle: This means they have 3 equal sides.

2. Isoceles triangle: They have only 2 equal sides.

3. Scalene triangle: The 3 sides are not equal

Based on their angles, we have 3 triangles.

a. Acute triangle

b. Obtuse triangle

c. Right angle triangle.

One of the way by which we can form a triangle, is by forming it with 2 acute angles and 1 right angle.

Answer 2

The correct option is;

A: 2 acute and 1 right

Explanation:

Here we have the definitions of the angles as follows;

The sum of angles in a triangle = 180°

An acute angle is an angle less than 90°

An obtuse angle is an angle more 90 ° but less 180°

A right angle triangle is an angle equal to 90°

∴ A right angle triangle is an angle = 90°

Therefore, we compare each of the options

A: 2 acute and 1 right = <90 +<90 +90 < 180 =180 or >180 Possible

B: 1 acute and 2 obtuse = 1<90 + > 90 +>90 > 180°

C: 1 acute and 2 right = <90 + 90 + 90 > 180

D: 1 acute + 1 right + 1 obtuse = <90 + 90 + >90 > 180

Therefore, the only possible correct option is A.