answersLogoWhite

0

Exterior angle of a triangle

Updated: 4/17/2023
User Avatar

Wiki User

12y ago

Best Answer

Exterior Angle Theorem

  • Exterior angle of a triangle

An exterior angle of a triangle is the angle formed by a side of the triangle and the extension of an adjacent side. In other words, it is the angle that is formed when you extend one of the sides of the triangle to create a new line, and then measure the angle between that new line and the adjacent side of the original triangle.

Each triangle has three exterior angles, one at each vertex of the triangle. The measure of each exterior angle is equal to the sum of the measures of the two interior angles that are not adjacent to it. This is known as the Exterior Angle Theorem.

  • For example, in the triangle below, the exterior angle at vertex C is equal to the sum of the measures of angles A and B

So, angle ACB (the exterior angle at vertex C) is equal to the sum of angles A and B.

Recomended for you: 𝕨𝕨𝕨.𝕕𝕚𝕘𝕚𝕤𝕥𝕠𝕣𝕖𝟚𝟜.𝕔𝕠𝕞/𝕣𝕖𝕕𝕚𝕣/𝟛𝟚𝟝𝟞𝟝𝟠/ℂ𝕠𝕝𝕝𝕖𝕟ℂ𝕠𝕒𝕝/

User Avatar

Collen Coal

Lvl 4
1y ago
This answer is:
User Avatar
More answers
User Avatar

MSK YOGA

Lvl 3
1y ago

The exterior angle of a triangle is an angle formed by one of the triangle's sides and the extension of an adjacent side. It is called an "exterior" angle because it lies outside the triangle.

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles of the triangle. This relationship is known as the exterior angle theorem.

For example, in the diagram below, the measure of angle A is equal to the sum of the measures of angles B and C.

[asy]

pair A,B,C;

A = (2,2);

B = (0,0);

C = (2,0);

draw(A--B--C--cycle);

label("$A$",A,N);

label("$B$",B,SW);

label("$C$",C,SE);

draw(A--C,dashed);

[/asy]

This answer is:
User Avatar

User Avatar

Joe goldberg

Lvl 4
1y ago
  • When any side of a triangle is extended, the angle that is formed with this side and its adjacent side is called the exterior angle of a triangle. There are three exterior angles in a triangle. It should be noted that each exterior angle forms a linear pair with its corresponding interior angle. We know that the interior angle of a triangle is formed inside it where the sides meet at a vertex. Observe the following figure to distinguish between the interior angles and the exterior angles of a triangle
This answer is:
User Avatar

User Avatar

bipulkumarwork123

Lvl 5
1y ago

In a triangle, an exterior angle is an angle formed by one side of the triangle and the extension of an adjacent side outside the triangle.

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles of the triangle. This property is known as the Exterior Angle Theorem, which states that:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles of the triangle.

In other words, if we label the three interior angles of a triangle as angle A, angle B, and angle C, and we label the exterior angle at vertex A as angle D, then we have:

Angle D = Angle B + Angle C

Similarly, we can find the measures of the other exterior angles by applying the same theorem.

This answer is:
User Avatar

User Avatar

Wiki User

12y ago

360 degrees minus the interior angle

This answer is:
User Avatar

Add your answer:

Earn +20 pts
Q: Exterior angle of a triangle
Write your answer...
Submit
Still have questions?
magnify glass
imp
Related questions

What is an exterior angle of a triangle?

It is: 180-interior angle = exterior angle


What is a Exterior angle of a triangle?

It is: 180-interior angle = exterior angle


What is an exterior angle for a triangle?

180 minus interior angle = exterior angle


How do you work out exterior angle for a triangle?

It is: 180-interior angle = exterior angle


Exterior angle property of a triangle?

measure of exterior angle of triangle is equal to sum of interior angles. for eg. In triangle ABC, angle C is exterior angle angle A and angle B are interior angles so, C=A+B


How do you find a missing exterior angle of a triangle?

At each vertex of a triangle, an exterior angle of the triangle may be formed by extending ONE SIDE of the triangle.


Can the exterior angle of triangle be straight angle?

When any side of triangle is extended outwards then exterior angle is formed. Sum of this exterior angle and adjacent interior angle = 180o. If exterior angle = 180o(straight angle) then interior adjacent angle is 0o which is not possible. So exterior angle can't be straight angle.


What is an exterior angle of a triangle and how does the measure of an exterior angle relate to the interior angles?

Exterior angle+interior angle=180 degrees and 180-exterior angle=interior angle


Is an exterior angle of a triangle always acute?

No :) Because one angle of the triangle is always acute and so the exterior has to be obtuse.


What is the Exterior Angle Theorem for a Triangle?

An exterior angle of a triangle is equal in measure to the sum of the other two interior angles.


What is The measurement of an exterior angle of a triangle is equal to the sum of?

Interior angle+exterior angle = 180 degrees


Which of these two regular polygons has the larger exterior angle a triangle or a heptagon?

It is the equilateral triangle that has the largest exterior angle of 120 degrees