Exterior angle of a triangle

Answer 1

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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Answer 2

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]

Answer 3

• 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

Answer 4

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.

Answer 5

360 degrees minus the interior angle