Exterior Angles of a Triangle Worksheet

Are you currently studying geometry or looking for additional practice on finding the exterior angles of a triangle? Look no further! This worksheet is designed to help you strengthen your understanding of this concept and provide you with ample opportunities to practice solving problems related to exterior angles.

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What is the definition of an exterior angle of a triangle?

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

How is the size of an exterior angle related to the sizes of the two remote interior angles?

The size of an exterior angle of a triangle is equal to the sum of the sizes of the two remote interior angles. In other words, the exterior angle is simply the sum of the two interior angles that are not adjacent to it.

How many exterior angles does a triangle have?

A triangle has three exterior angles.

Can an exterior angle of a triangle be greater than 180 degrees? Why or why not?

No, an exterior angle of a triangle cannot be greater than 180 degrees. The sum of the measures of the three interior angles of a triangle always adds up to 180 degrees. Therefore, the exterior angle formed by extending one side of a triangle will always be equal to the sum of the two non-adjacent interior angles of the triangle. Since the maximum measure of an interior angle of a triangle is 180 degrees, the exterior angle cannot exceed this value.

How can you determine the measure of an exterior angle of a triangle if you know the measures of the other two interior angles?

To determine the measure of an exterior angle of a triangle, subtract the sum of the two given interior angles from 180 degrees. The sum of the interior angles of a triangle is always 180 degrees, so subtracting the sum of the two given interior angles from 180 degrees will give you the measure of the exterior angle.

Is it possible for an exterior angle of a triangle to be smaller than either of the remote interior angles? Explain.

No, it is not possible for an exterior angle of a triangle to be smaller than either of the remote interior angles. By definition, the exterior angle of a triangle is always larger than either of the remote interior angles because it forms a linear pair with one of the interior angles and is supplementary to it. Thus, the exterior angle must be greater in measure than the interior angle it supplements.

How do exterior angles of a triangle relate to the properties of parallel lines?

The exterior angles of a triangle are equal to the sum of the two remote interior angles of the triangle. When a transversal intersects two parallel lines, the exterior angle theorem states that the exterior angle formed is equal to the interior opposite angle. This means that if two lines are parallel, then the exterior angle between them and a transversal will equal the remote interior angle of the triangle formed by the parallel lines and the transversal.

Can the exterior angle at one vertex of a triangle be equal to the interior angle of another vertex? Why or why not?

No, the exterior angle at one vertex of a triangle cannot be equal to the interior angle of another vertex because the sum of the interior angles of a triangle is always 180 degrees, while the exterior angle at a vertex is supplementary to the adjacent interior angle and therefore cannot be equal to it.

When does the sum of the measures of the exterior angles of a triangle equal 360 degrees?

The sum of the measures of the exterior angles of a triangle will always be 360 degrees, since the exterior angle at each vertex of a triangle is equal in measure to the sum of the two remote interior angles. Therefore, as the sum of the interior angles of a triangle is always 180 degrees, the exterior angles will always add up to 360 degrees.

How can the concept of exterior angles of a triangle be extended to other polygons?

The concept of exterior angles of a polygon can be extended by recognizing that the exterior angle of any polygon is the angle formed between one side of the polygon and the extension of its adjacent side. This means that for any polygon, the sum of the exterior angles is always 360 degrees. This property holds true for all polygons, not just for triangles, making it a useful tool for calculating interior angles of polygons or solving geometric problems involving angles.