What is the exterior angle theorem used for?
The exterior angle theorem states that when a triangle’s side is extended, the resultant exterior angle formed is equal to the sum of the measures of the two opposite interior angles of the triangle. The theorem can be used to find the measure of an unknown angle in a triangle.
Which relationship is supported by the exterior angle theorem?
The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles. Remember that the two non-adjacent interior angles opposite the exterior angle are sometimes referred to as remote interior angles.
What is the sum of the exterior angles theorem?
If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360° .
What is the relationship between the measure of the exterior angle of a triangle and its remote interior angles?
The exterior angle theorem states that: The measure of an exterior angle of a triangle is supplementary to its adjacent interior angle. The sum of the remote interior angles must equal the measure of the exterior angle of the triangle.
What is exterior angle example?
An exterior angle of a triangle is equal to the sum of the two opposite interior angles. Example: Find the values of x and y in the following triangle. y + 92° = 180° (interior angle + adjacent exterior angle = 180°.)
How do you prove exterior angles of property?
The exterior angle of a given triangle equals the sum of the opposite interior angles of that triangle. If an equivalent angle is taken at each vertex of the triangle, the exterior angles add to 360° in all the cases. In fact, this statement is true for any given convex polygon and not just triangles.
What is exterior angle property of a triangle?
What is the exterior angle property? If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
What does the angle angle criterion tell you about the relationship between two triangles?
The Angle-Angle (AA) Criterion states that if two angles in one triangle are congruent to two angles in another triangle, the two triangles are similar triangles.
What is the relation of the measure of an exterior angle of a triangle to the measure of its corresponding remote interior angle?
The exterior angle theorem is Proposition 1.16 in Euclid’s Elements, which states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
What can you conclude about the relationship of the measures of the remote interior angles to the exterior angle?
Since the angle sum in a triangle is also 180 degrees, the exterior angle must have a measure equal to the sum of the remaining angles, called the remote interior angles.
Is the measure of an exterior angle is equal to the sum of its remote interior angles?
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (Non-adjacent interior angles may also be referred to as remote interior angles.)
What is the exterior angle theorem?
The exterior angle theorem mentions that the exterior angle when one particular side is extended is equal to the sum of the two opposite interior angles.
What is the sum of the measures of the exterior angles?
As a result, the total of 1, 2, 3, 4, and 5 equals 36 0 o. As a result, regardless of the number of sides in the polygons, the sum of the measures of the exterior angles equals 36 0 o. Let us prove that if a polygon is a convex polygon, then the sum of its exterior angles (one at each vertex) is equal to 36 0 o.
What is the sum of exterior angles of a convex polygon?
The polygon exterior angle sum theorem states that the sum of all exterior angles of a convex polygon is equal to 360º. Sum of exterior angles of polygon = 360º The formula for the exterior angle of a regular polygon with n number of sides can be given as,
How do you do the exterior angle theorem with toothpicks?
Give each group a set of toothpicks to work with. Allow them to cut the toothpicks or tape them together to construct triangles of different sizes. They should create at least three different toothpick representations showing how the exterior angle theorem works within triangles.