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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.

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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]

Lvl 4

- 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

Lvl 5

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.

360 degrees minus the interior angle

Q: Exterior angle of a triangle

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It is: 180-interior angle = exterior angle

It is: 180-interior angle = exterior angle

180 minus interior angle = exterior angle

It is: 180-interior angle = exterior angle

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

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

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.

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

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

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

Interior angle+exterior angle = 180 degrees

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