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Exterior Angle The Exterior Angle is the angle between any side of a shape, and a line extended from the next side. Another example: When we add up the Interior Angle and Exterior Angle we get a Straight Angle (180°), so they are "Supplementary Angles".
- Exterior Angles of Polygons
The Exterior Angles of a Polygon add up to 360°...
- Straight Angle
Read more about Angles 9155, 3293, 8992, 1772, 3281, 3292,...
- Supplementary Angles
How to remember which is which? Well, alphabetically they...
- Interior Angles of Polygons
The Interior Angles of a Triangle add up to 180. Interior...
- Exterior Angle Theorem
Math explained in easy language, plus puzzles, games,...
- Exterior Angle
Illustrated definition of Exterior Angle: The angle between...
- Exterior Angles of Polygons
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. Learn about exterior angle theorem - statement, explanation, proof and solved examples.
- What Is The Exterior Angle Theorem?
- Exterior Angle Theorem Statement
- Exterior Angle Inequality Theorem
- Conclusion
- Solved Examples on Exterior Angle Theorem
Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles. The remote interior angles or opposite interior angles are the angles that are non-adjacent with the exterior angle. A triangle is a polygon with three sides. When we extend any side of a triangle, an angle is formed ...
According to the exterior angle theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite (remote) interior angles. Take a look at the triangle shown in the figure given below. ∠BCD is the exterior angle and its two opposite interior angles are ∠A and ∠B. According to the exterior angle theorem,...
The exterior angle inequality theorem states that the measure of any exterior angle of a triangle is greater than each of the opposite interior angles. This theorem holds true for all the six exterior angles of a triangle.
In this article, we learned about the exterior angle theorem, its statement and proof. We also learned the exterior angle inequality theorem. Let’s solve a few examples and practice problems based on these concepts.
1. Find the value of ∠ACB in the following figure. Solution: ∠CAD is the exterior angle of ΔABC. By the exterior angle theorem, ∠CAD=∠ABC+∠ACB 120∘=40∘+∠ACB ∠ACB=120∘−40∘=80∘ 2. Find the value of xin the following figure. Solution: (8x+25)∘ is the exterior angle of ΔPQR. Its remote interior angles are (2x+10)∘ and (5x+20)∘. By the exterior angle th...
Exterior angles: Exterior angles are the angles formed outside a shape, between any side of a shape and an extended adjacent side. Here, ∠ACD is an exterior angle. Complementary and Supplementary Angles: Complementary angles: Angles that add up to 90° (a right angle) are called complementary angles. Here, ∠BXC and ∠CXD are complementary ...
- The angles are of two types based on the direction of the cycle: Positive Angles: Positive angles are measured in the anticlockwise or counterclock...
- Angles sharing a vertex and one side of a line add up to 180°. Angles with a common vertex occupying the space around a point add up to 360°.
- Types of angles based on the measurement are: Right angle Straight angle Reflex angle Obtuse angle Acute angle Complete angle
- Engineers and architects use angles for building, measurement, designing, etc. Architects and engineers use it to design roads, buildings, and spor...
Illustrated definition of Exterior Angle: The angle between any side of a shape, and a line extended from the next side.
The exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles). This is also known as the Exterior Angle theorem . The sum of all the exterior angles of a triangle is 360°.
Exterior angles are angles that are parallel to the inner angles of a polygon but lie on the outside of it. The measure of an exterior angle is equal to the sum of the two internal opposite angles. In the given image ‘a’ and ‘b’ are interior angles and ‘d’ is the exterior angle.
