Question

Under which angle conditions could a triangle exist? Check all that apply.
3 acute angles
2 acute angles, 1 right angle
1 acute angle, 1 right angle, 1 obtuse angle
1 acute angle, 2 obtuse angles
2 acute angles, 1 obtuse angle

Answer 1

an acute angle is <90 degrees
a right angle is equal to 90 degrees
an obtuse angle is >90 degrees
Any triangle has angles adding to 180 degrees

therefore three acute angles, eg. 60, 60 and 60 degrees can make up a triangle

2 acute angles and a right angle, say 45 and 45 degrees and 90 degrees make a triangle

any obtuse angle + a right angle will be larger than 180 degrees, so no triangle can exist. another acute angle will make the number of degrees even larger

any 2 obtuse angles will make a number larger than 180 degrees, so with an acute angle is impossible

2 acute and an obtuse angle is possible, say 40, 40 and 100 degrees

Answer 2

The correct answer is

3 acute angles

2 acute angles, 1 right angle

2 acute angles, 1 obtuse angle

Further Explanation

The basic properties of triangles include

• In a triangle, all the sum of the angle is 180 degree and it is also referred to as angle sum property.
• In a triangle, the sum of the two sides is greater than the sum of the third side.
• In a triangle, the longest side is the side that opposite the largest angle and vice versa.

A triangle refers to a closed figure with a three-line segment and three angles.  

The three types of a triangle based on size are:

Equilateral triangle , Isosceles triangle  and Scalene triangle

• An equilateral triangle is a triangle where the lengths of all the three sides are equal
• An isosceles triangle is a triangle where its two sides are equal
• A scalene triangle is a triangle that has three sides with different length

However, the three types of a triangle based on angles include:

• Acute-angled triangle: in Acute-angled triangle, all its angle are acute
• Obtuse-angled triangle: in Obtuse-angled triangle, one its angle is obtuse
• Right-angled triangle: in the Right-angled triangle, one of its angles is a right angle.

Therefore, the correct answer is 3 acute angles, 2 acute angles, 1 right angle, 2 acute angles, 1 obtuse angle

LEARN MORE:

• Under which angle conditions could a triangle exist? Check all that apply. https://brainly.com/question/10334248
• 1/2 of an obtuse angle is a(n): A. Obtuse angle. B. Acute angle https://brainly.com/question/10670855

KEYWORDS:

• right-angled triangle
• acute angles
• 2 acute angles
• obtuse angle
• a scalene triangle