Obtuse Triangle Definition

An obtuse triangle is a triangle that has one obtuse angle (greater than 90° 90° degrees and less than 180° 180° degrees) and two acute angles (each of which is less than 90° 90° degrees). The sum of all three angles together is 180° 180° degrees.

Practice Obtuse Triangle

Examples with solutions for Obtuse Triangle

Exercise #1

What kid of triangle is given in the drawing?

90°90°90°AAABBBCCC

Video Solution

Step-by-Step Solution

The measure of angle C is 90°, therefore it is a right angle.

If one of the angles of the triangle is right, it is a right triangle.

Answer

Right triangle

Exercise #2

What kind of triangle is given in the drawing?

404040707070707070AAABBBCCC

Video Solution

Step-by-Step Solution

As all the angles of a triangle are less than 90° and the sum of the angles of a triangle equals 180°:

70+70+40=180 70+70+40=180

The triangle is isosceles.

Answer

Isosceles triangle

Exercise #3

What kid of triangle is the following

393939107107107343434AAABBBCCC

Video Solution

Step-by-Step Solution

Given that in an obtuse triangle it is enough for one of the angles to be greater than 90°, and in the given triangle we have an angle C greater than 90°,

C=107 C=107

Furthermore, the sum of the angles of the given triangle is 180 degrees so it is indeed a triangle:

107+34+39=180 107+34+39=180

The triangle is obtuse.

Answer

Obtuse Triangle

Exercise #4

What kind of triangle is given in the drawing?

999555999AAABBBCCC

Video Solution

Step-by-Step Solution

Given that sides AB and AC are both equal to 9, which means that the legs of the triangle are equal and the base BC is equal to 5,

Therefore, the triangle is isosceles.

Answer

Isosceles triangle

Exercise #5

Which kind of triangle is given in the drawing?

666666666AAABBBCCC

Video Solution

Step-by-Step Solution

As we know that sides AB, BC, and CA are all equal to 6,

All are equal to each other and, therefore, the triangle is equilateral.

Answer

Equilateral triangle

Exercise #6

What kind of triangle is given here?

111111555AAABBBCCC5.5

Video Solution

Step-by-Step Solution

Since none of the sides have the same length, it is a scalene triangle.

Answer

Scalene triangle

Exercise #7

Calculate the size of angle X given that the triangle is equilateral.

XXXAAABBBCCC

Video Solution

Step-by-Step Solution

Remember that the sum of angles in a triangle is equal to 180.

In an equilateral triangle, all sides and all angles are equal to each other.

Therefore, we will calculate as follows:

x+x+x=180 x+x+x=180

3x=180 3x=180

We divide both sides by 3:

x=60 x=60

Answer

60

Exercise #8

Given the values of the sides of a triangle, is it a triangle with different sides?

9.19.19.19.59.59.5AAABBBCCC9

Video Solution

Step-by-Step Solution

As is known, a scalene triangle is a triangle in which each side has a different length.

According to the given information, this is indeed a triangle where each side has a different length.

Answer

Yes

Exercise #9

Choose the appropriate triangle according to the following:

Angle B equals 90 degrees.

Video Solution

Step-by-Step Solution

Let's note in which of the triangles angle B forms a right angle, meaning an angle of 90 degrees.

In answers C+D, we can see that angle B is smaller than 90 degrees.

In answer A, it is equal to 90 degrees.

Answer

AAABBBCCC

Exercise #10

Is the triangle in the drawing a right triangle?

Video Solution

Step-by-Step Solution

It can be seen that all angles in the given triangle are less than 90 degrees.

In a right-angled triangle, there needs to be one angle that equals 90 degrees

Since this condition is not met, the triangle is not a right-angled triangle.

Answer

No

Exercise #11

Is the triangle in the drawing a right triangle?

Step-by-Step Solution

Due to the presence of the 90 degree angle symbol we can determine that this is indeed a right-angled triangle.

Answer

Yes

Exercise #12

In a right triangle, the sum of the two non-right angles is...?

Video Solution

Step-by-Step Solution

In a right-angled triangle, there is one angle that equals 90 degrees, and the other two angles sum up to 180 degrees (sum of angles in a triangle)

Therefore, the sum of the two non-right angles is 90 degrees

90+90=180 90+90=180

Answer

90 degrees

Exercise #13

What kind of triangle is the following

606060606060606060AAABBBCCC

Video Solution

Step-by-Step Solution

Since in the given triangle all angles are equal, all sides are also equal.

It is known that in an equilateral triangle the measure of the angles will always be equal to 60° since the sum of the angles in a triangle is 180 degrees:

60+60+60=180 60+60+60=180

Therefore, it is an equilateral triangle.

Answer

Equilateral triangle

Exercise #14

Given an equilateral triangle:

555

What is its perimeter?

Video Solution

Step-by-Step Solution

Since the triangle is equilateral, that is, all sides are equal to each other.

The perimeter of the triangle is equal to the sum of all sides together, the perimeter of the triangle in the drawing is equal to:

5+5+5=15 5+5+5=15

Answer

15

Exercise #15

Below is an equilateral triangle:

XXX

If the perimeter of the triangle is 33 cm, then what is the value of X?

Video Solution

Step-by-Step Solution

We know that in an equilateral triangle all sides are equal.

Therefore, if we know that one side is equal to X, then all sides are equal to X.

We know that the perimeter of the triangle is 33.

The perimeter of the triangle is equal to the sum of the sides together.

We replace the data:

x+x+x=33 x+x+x=33

3x=33 3x=33

We divide the two sections by 3:

3x3=333 \frac{3x}{3}=\frac{33}{3}

x=11 x=11

Answer

11