What are the remote and interior angles?It's all about extending a side of the triangle Show
An exterior angle of a triangle, or any polygon, is formed by extending one of the sides. In a triangle, each exterior angle has two remote interior angles . The remote interior angles are just the two angles that are inside the triangle and opposite from the exterior angle.  The Formula As the picture above shows, the formula for remote and interior angles states that the measure of a an exterior angle $$ \angle A $$ equals the sum of the remote interior angles. To rephrase it, the angle 'outside the triangle' (exterior angle A) equals D + C (the sum of the remote interior angles). $\begingroup$ < = angle An exterior angle is formed between a side and the extension of a side. It will always be a linear pair with an internal angle. In the diagram below, <4 is the exterior angle. The exterior angle theorem states that the external angle is equal to the sum of the two remote angles. The remote angles are those interior angles that are not adjacent to the exterior angle so in this case <1 and <2 are the remote angles. m<1 + m<2 = m<4, Explain why this is true please !! asked Sep 30, 2015 at 21:19
$\endgroup$ 1 $\begingroup$ Angle $1$ + Angle $2$ + Angle $3$ = 180 Angle $3$ + Angle $4$ = 180. The result is that Angle $4$ = Angle $1$ + Angle $2$. answered Sep 30, 2015 at 21:22
Oria GruberOria Gruber 12.3k8 gold badges44 silver badges95 bronze badges $\endgroup$ 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. To apply the theorem, we first need to identify the exterior angle and then the associated two remote interior angles of the triangle. What is Exterior Angle Theorem?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle. Let us recall a few common properties about the angles of a triangle: A triangle has 3 internal angles which always sum up to 180 degrees. It has 6 exterior angles and this theorem gets applied to each of the exterior angles. Note that an exterior angle is supplementary to its adjacent interior angle as they form a linear pair of angles. Exterior angles are defined as the angles formed between the side of the polygon and the extended adjacent side of the polygon. We can verify the exterior angle theorem with the known properties of a triangle. Consider a Δ ABC. The three angles a + b + c = 180 (angle sum property of a triangle) ----- Equation 1 c= 180 - (a+b) ----- Equation 2 (rewriting equation 1) e = 180 - c----- Equation 3 (linear pair of angles) Substituting the value of c in equation 3, we get e = 180 - [180 - (a + b)] e = 180 - 180 + (a + b) e = a + b Hence verified. Proof of Exterior Angle TheoremConsider a ΔABC. a, b and c are the angles formed. Extend the side BC to D. Now an exterior angle ∠ACD is formed. Draw a line CE parallel to AB. Now x and y are the angles formed, where, ∠ACD = ∠x + ∠y
Hence proved that the exterior angle of a triangle is equal to the sum of the two opposite interior angles. Exterior Angle Inequality TheoremThe exterior angle inequality theorem states that the measure of any exterior angle of a triangle is greater than either of the opposite interior angles. This condition is satisfied by all the six external angles of a triangle. Related Articles Check out a few interesting articles related to Exterior Angle Theorem.
Important notes
FAQs on Exterior Angle TheoremWhat is the Exterior Angle Theorem?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle. The remote interior angles are also called opposite interior angles. How do you use the Exterior Angle Theorem?To use the exterior angle theorem in a triangle we first need to identify the exterior angle and then the associated two remote interior angles of the triangle. A common mistake of considering the adjacent interior angle should be avoided. After identifying the exterior angles and the related interior angles, we can apply the formula to find the missing angles or to establish a relationship between sides and angles in a triangle. What are Exterior Angles?An exterior angle of a triangle is formed when any side of a triangle is extended. There are 6 exterior angles of a triangle as each of the 3 sides can be extended on both sides and 6 such exterior angles are formed. What is the Exterior Angle Inequality Theorem?The measure of an exterior angle of a triangle is always greater than the measure of either of the opposite interior angles of the triangle. What is the Exterior Angle Property?An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles. The sum of the exterior angle and the adjacent interior angle that is not opposite is equal to 180º. What is the Exterior Angle Theorem Formula?The sum of the exterior angle = the sum of two non-adjacent interior opposite angles. An exterior angle of a triangle is equal to the sum of its two opposite non-adjacent interior angles. Where Should We Use Exterior Angle Theorem?Exterior angle theorem could be used to determine the measures of the unknown interior and exterior angles of a triangle. Do All Polygons Exterior Angles Add up to 360?The exterior angles of a polygon are formed when a side of a polygon is extended. All the exterior angles in all the polygons sum up to 360º. What are the two remote interior angles?Remote Interior Angles
The remote interior angles are the two angles on the inside of the triangle that are not touching the exterior angle. Think of them as the "far away" inside angles, they are on the other side of the triangle, away from the exterior angle.
What are the remote interior angles of the marked exterior angle?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.
How do you name remote interior angles?Remote interior angles are those that don't share a vertex or corner of a triangle with the exterior angle. In our example, angle d is an exterior angle, and angle a and angle b are the remote interior angles of angle d.
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In terms of the exterior angle name the two remote interior angles
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