Exterior angles of a triangle - Examples, Exercises and Solutions

Question Types:
Parts of a Triangle: Classify a triangle by its sidesParts of a Triangle: Is it possible...?Parts of a Triangle: Using the median to calculate the perimeterParts of a Triangle: Using the theorem: The median of a triangle divides it into two triangles of the same areaSum and Difference of Angles: Is it possible...?Sum and Difference of Angles: Isosceles triangleParts of a Triangle: Median in an isosceles triangle - propertiesParts of a Triangle: Using parallel linesParts of a Triangle: Determine the size of the given anglesParts of a Triangle: Identify the greater valueParts of a Triangle: Median in a right-angled triangleParts of a Triangle: Using properties of the medianSum and Difference of Angles: Using variablesParts of a Triangle: Identifying the sides in a triangle using median and heightSum and Difference of Angles: Calculate Angles in QuadrilateralsSum and Difference of Angles: Identifying and defining elementsParts of a Triangle: Calculate Angles in QuadrilateralsParts of a Triangle: True / falseSum and Difference of Angles: Using quadrilateralsSum and Difference of Angles: Angle bisectorParts of a Triangle: Identifying sides in a triangleSum and Difference of Angles: Applying the formulaSum and Difference of Angles: Generate a random angleParts of a Triangle: Using angles in a triangleSum and Difference of Angles: Identify the greater valueSum and Difference of Angles: Using angles in a triangleParts of a Triangle: Identifying and defining elementsParts of a Triangle: Finding the size of angles in a triangleSum and Difference of Angles: Finding the size of angles in a triangle

The exterior angle of a triangle is the one that is found between the original side and the extension of the side.
The exterior angle is equal to the sum of the two interior angles of the triangle that are not adjacent to it.

It is defined as follows:

A1 - Exterior angle of a triangle

α=A+Bα=∢A+∢B

Practice Exterior angles of a triangle

Examples with solutions for Exterior angles of a triangle

Exercise #1

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 #2

Can a triangle have two right angles?

Video Solution

Step-by-Step Solution

The sum of angles in a triangle is 180 degrees. Since two angles of 90 degrees equal 180, a triangle can never have two right angles.

Answer

No

Exercise #3

Look at the two triangles below. Is EC a side of one of the triangles?

AAABBBCCCDDDEEEFFF

Video Solution

Step-by-Step Solution

Every triangle has 3 sides, let's go over the triangle on the left side:

Its sides are: AB, BC, CA

This means that in this triangle, side EC does not exist.

Let's go over the triangle on the right side:

Its sides are: ED, EF, FD

This means that in this triangle, side EC does not exist.

Therefore, EC is not a side in either of the triangles.

Answer

No.

Exercise #4

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 #5

What is the value of the void angle?

160

Video Solution

Step-by-Step Solution

The empty angle is an angle adjacent to 160 degrees.

Remember that the sum of adjacent angles is 180 degrees.

Therefore, the value of the empty angle will be:

180160=20 180-160=20

Answer

20

Exercise #6

What type of angle is α \alpha ?

αα

Step-by-Step Solution

Let's remember that an acute angle is smaller than 90 degrees, an obtuse angle is larger than 90 degrees, and a straight angle equals 180 degrees.

Since in the drawing we have lines perpendicular to each other, the marked angles are right angles, each equal to 90 degrees.

Answer

Straight

Exercise #7

Which of the following is the height in triangle ABC?

AAABBBCCCDDD

Video Solution

Step-by-Step Solution

Let's remember the definition of height of a triangle:

A height is a straight line that descends from the vertex of a triangle and forms a 90-degree angle with the opposite side.

The sides that form a 90-degree angle are sides AB and BC. Therefore, the height is AB.

Answer

AB

Exercise #8

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

Video Solution

Step-by-Step Solution

We add the three angles to see if they equal 180 degrees:

30+60+90=180 30+60+90=180
The sum of the angles equals 180, so they can form a triangle.

Answer

Yes

Exercise #9

ABC is an isosceles triangle.

AD is the median.

What is the size of angle ADC ∢\text{ADC} ?

AAABBBCCCDDD

Video Solution

Step-by-Step Solution

In an isosceles triangle, the median to the base is also the height to the base.

That is, side AD forms a 90° angle with side BC.

That is, two right triangles are created.

Therefore, angle ADC is equal to 90 degrees.

Answer

90

Exercise #10

Given the following triangle:

Write down the height of the triangle ABC.

AAABBBCCCEEEDDD

Video Solution

Step-by-Step Solution

An altitude in a triangle is the segment that connects the vertex and the opposite side, in such a way that the segment forms a 90-degree angle with the side.

If we look at the image it is clear that the above theorem is true for the line AE. AE not only connects the A vertex with the opposite side. It also crosses BC forming a 90-degree angle. Undoubtedly making AE the altitude.

Answer

AE

Exercise #11

Angle A equals 90°.
Angle B equals 115°.
Angle C equals 35°.

Can these angles form a triangle?

Video Solution

Step-by-Step Solution

We add the three angles to see if they are equal to 180 degrees:

90+115+35=240 90+115+35=240
The sum of the given angles is not equal to 180, so they cannot form a triangle.

Answer

No.

Exercise #12

Angle A equals 56°.
Angle B equals 89°.
Angle C equals 17°.

Can these angles make a triangle?

Video Solution

Step-by-Step Solution

We add the three angles to see if they are equal to 180 degrees:

56+89+17=162 56+89+17=162

The sum of the given angles is not equal to 180, so they cannot form a triangle.

Answer

No.

Exercise #13

Below is an equilateral triangle.

Calculate X.

X+5X+5X+5AAABBBCCC

Video Solution

Step-by-Step Solution

Since in an equilateral triangle all sides are equal and all angles are equal. It is also known that in a triangle the sum of angles is 180°, we can calculate X in the following way:

X+5+X+5+X+5=180 X+5+X+5+X+5=180

3X+15=180 3X+15=180

3X=18015 3X=180-15

3X=165 3X=165

Let's divide both sides by 3:

3X3=1653 \frac{3X}{3}=\frac{165}{3}

X=55 X=55

Answer

55

Exercise #14

What is the size of angle ABC?

DBC = 100°

DDDBBBCCCAAA10040

Video Solution

Step-by-Step Solution

Given that angle DBC is equal to 100 degrees. Let's look at the letters and note that angle ABC is given and equals 40 degrees

Answer

40

Exercise #15

Indicates which angle is greater

Video Solution

Step-by-Step Solution

Answer B is correct because the more closed the angle is, the more acute it is (less than 90 degrees), meaning it's smaller.

The more open the angle is, the more obtuse it is (greater than 90 degrees), meaning it's larger.

Answer

Topics learned in later sections

  1. Area
  2. The sides or edges of a triangle
  3. Triangle Height
  4. The Sum of the Interior Angles of a Triangle
  5. Types of Triangles
  6. Obtuse Triangle
  7. Equilateral triangle
  8. Identification of an Isosceles Triangle
  9. Scalene triangle
  10. Acute triangle
  11. Isosceles triangle
  12. The Area of a Triangle
  13. Area of a right triangle
  14. Area of Isosceles Triangles
  15. Area of a Scalene Triangle
  16. Area of Equilateral Triangles
  17. Perimeter
  18. Triangle
  19. Perimeter of a triangle