Exterior angles are defined as the angle formed between the next of the polygon and also the extended nearby side the the polygon. The exterior angle theorem states that as soon as a triangle's next is extended, the result exterior angle created is same to the amount of the steps of the two opposite interior angles the the triangle. The theorem have the right to be provided to find the measure of an unknown edge in a triangle. To apply the theorem, we first need to determine the exterior angle and then the associated two remote inner angles of the triangle.
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|1.||What is Exterior angle Theorem?|
|2.||Proof that Exterior edge Theorem|
|3.||Exterior edge Inequality Theorem|
|4.||FAQs top top Exterior edge Theorem|
What is Exterior angle Theorem?
The exterior angle theorem says that the measure of one exterior angle is same to the amount of the actions of the 2 opposite(remote) internal angles that the triangle. Let us recall a few common properties around the angle of a triangle: A triangle has 3 inner angles which always sum as much as 180 degrees. It has 6 exterior angles and also this theorem gets applied to each of the exterior angles. Note that one exterior angle is supplementary to its surrounding interior angle together they form a direct pair the angles.
We have the right to verify the exterior angle theorem v the well-known properties of a triangle. Consider a Δ ABC.
The three angles a + b + c = 180 (angle sum home of a triangle) ----- Equation 1
c= 180 - (a+b) ----- Equation 2 (rewriting equation 1)
e = 180 - c----- Equation 3 (linear pair that angles)
Substituting the worth of c in equation 3, us get
e = 180 - <180 - (a+b)>
e = 180 - 180 + (a + b)
e = a + b
Proof that Exterior angle Theorem
Consider a ΔABC. A, b and c space the angles formed. Expand the next BC come D. Now an exterior angle ∠ACD is formed. Attract a heat CE parallel come AB. Now x and also y space the angle formed, where, ∠ACD = ∠x + ∠y
|∠a = ∠x||Pair of alternative angles. (Since BA is parallel come CE and also AC is the transversal).|
|∠b = ∠y||Pair of corresponding angles. (Since BA is parallel to CE and also BD is the transversal).|
|∠a + ∠b = ∠x + ∠y||From the over statements|
|∠ACD = ∠x + ∠y||From the building and construction of CE|
|∠a + ∠b = ∠ACD||From the over statements|
Hence verified that the exterior angle of a triangle is same to the sum of the two opposite inner angles.
Exterior edge Inequality Theorem
The exterior angle inequality theorem states that the measure up of any kind of exterior edge of a triangle is higher than one of two people of the opposite internal angles. This condition is to solve by all the six external angles the a triangle.
Exterior angles Theorem related Articles
Check out a few interesting short articles related to Exterior angle Theorem.
Important notesThe exterior edge theorem claims that the measure of an exterior angle is equal to the sum of the actions of the two remote internal angles the the triangle.The exterior edge inequality theorem claims that the measure up of any exterior angle of a triangle is better than either of the opposite interior angles.The exterior angle and the adjacent interior angle are supplementary. All the exterior angle of a triangle sum up come 360º.
Example 1: find the worths of x and also y by using the exterior angle theorem the a triangle.
∠x is the exterior angle.
∠x + 92 = 180º (linear pair of angles)
∠x = 180 - 92 = 88º
Applying the exterior angle theorem, us get, ∠y + 41 = 88
∠y = 88 - 41 = 47º
Therefore, the values of x and y space 88º and 47º respectively.
Example 2: find ∠BAC and also ∠ABC.
160º is an exterior edge of the Δ ABC. So, by using the exterior edge theorem, we have, ∠BAC + ∠ABC = 160º
x + 3x = 160º
4x = 160º
x = 40º
Therefore, ∠BAC = x = 40º and ∠ABC = 3xº = 120º
Example 3: discover ∠ BAC, if ∠CAD = ∠ADC
Solving the linear pair in ~ vertex D, we gain ∠ADC + ∠ADE = 180º
∠ADC = 180º - 150º = 30º
Using the angle amount property, for Δ ACD,
∠ADC + ∠ACD + ∠CAD = 180º
∠ACD = 180 - ∠CAD -∠ADC
180º - ∠ADC -∠ADC (given ∠CAD= ∠ADC)
180º - 2∠ADC
180º - 2 × 30º
∠ACD = 180º - 60º = 120º
∠ACD is the exterior edge of ∠ABC
Using the exterior edge theorem, because that Δ ABC, ∠ACD = ∠ABC + ∠BAC
120º = 60º + ∠BAC
Therefore, ∠BAC = 120º - 60º = 60º.
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FAQs on Exterior edge Theorem
What is the Exterior edge Theorem?
The exterior edge theorem states that the measure up of one exterior edge is equal to the sum of the actions of the 2 remote internal angles of the triangle. The remote interior angles are also called opposite inner angles.
How carry out you use the Exterior edge Theorem?
To usage the exterior edge theorem in a triangle we first need to recognize the exterior angle and then the linked two remote internal angles of the triangle. A typical mistake that considering the adjacent interior angle must be avoided. After identify the exterior angles and also the related inner angles, us can use the formula to discover the lacking angles or to create a relationship in between sides and also angles in a triangle.
What room Exterior Angles?
An exterior edge of a triangle is created when any type of side of a triangle is extended. There space 6 exterior angles of a triangle as each of the 3 sides have the right to be prolonged on both sides and 6 together exterior angles space formed.
What is the Exterior angle Inequality Theorem?
The measure up of one exterior angle of a triangle is always greater 보다 the measure up of one of two people of the opposite inner angles that the triangle.
What is the Exterior angle Property?
An exterior angle of a triangle is equal to the amount of its two opposite non-adjacent interior angles. The sum of the exterior angle and the surrounding interior angle that is no opposite is equal to 180º.
What is the Exterior angle Theorem Formula?
The sum of the exterior edge = the sum of 2 non-adjacent internal opposite angles. An exterior edge of a triangle is same to the amount of its 2 opposite non-adjacent interior angles.
Where must We use Exterior angle Theorem?
Exterior edge theorem might be provided to determine the steps of the unknown interior and also exterior angles of a triangle.
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Do every Polygons Exterior Angles add up come 360?
The exterior angle of a polygon are created when a side of a polygon is extended. All the exterior angle in all the polygons sum up to 360º.