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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
Sometimes people say "You did a complete 180 on that!" ......
- 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
- What Is An angle?
- Symbol of Angle
- Parts of Angles
- Types of Angles
- Interior and Exterior Angles
- Complementary and Supplementary Angles
- How to Construct An Angle
- Real-Life Application of Angles
- Angles Around Us
- Solved Examples on Angles
An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’ meaning “corner.”
The symbol ∠ represents an angle. Angles are measured in degrees (°) using a protractor. For example, 45 degreesis represented as 45°
Vertex:A vertex is a corner of an angle, a point where two lines/sides meet. O is the vertex in the given figure.Arms:The two sides of the angle, joined at a common endpoint. OA and OB are arms of an angle.Initial Side: Also known as the reference line, a straight line from where an angle is drawn. OB is the reference line.Terminal Side: The side up to which the angle measurementis done. In the given diagram below, OA is the terminal side.Based on their measurements, here are the different types of angles: 1. An acute angle measures less than90° at the vertex. 2. An obtuse angleis between 90° and 180°. 3. A right angleprecisely measures 90° at the vertex. 4. An angle measuring exactly 180° is a straight angle. 5. A reflex anglemeasures between 180°- 360°. 6. `A complete angle measur...
Interior angles: Interior Angles are the angles formed within or inside a shape. Here, ∠ABC, ∠BCA and ∠CAB are interior angles. 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 angles: Angles that add up to 90° (a right angle) are called complementary angles. Here, ∠BXC and ∠CXD are complementary angles. Supplementary angles: Angles that add up to 180° (a straight angle) are called supplementary angles. Here, ∠AXD and ∠CXD are supplementary angles.
Draw a ray OA of any length.Now, place the protractor at that point, and its midpoint should touch the marked point O.Now mark the point as B on the top circular part of a protractor, according to the preferred angle for example 40°.Draw a straight line joining those two points, O and B.Engineers construct buildings, bridges, houses, monuments, etc., using angle measurement.Athletes use its concept in sports to enhance their performance.Carpenters use it to make equipment like doors, chairs, sofas, tables, etc.Artists use their measurement knowledge to sketch or create art pieces.There are many daily life examples of an angle, such as cloth-hangers, arrowheads, scissors, partly opened doors, pyramids, edge of a table, the edge of a ruler, etc.
Example 1: Find missing angle x in the figure. Solution: We can see a ∠x + 35° = 90° ∠x = (90 – 35)° = 55° Example 2: Solve for x. Solution: 5x – 70 = 105 (alternate angles) 5x = 175 Therefore, x = 35° Example 3: In a triangle ABC, ∠A = 90 and ∠B = 30. Find ∠C. Solution: The sum of all 3 interior angles of a triangle is equalto 180°. Hence, 90° + 3...
- Congruent angles. Any two angles, no matter their orientation, that have equal measures (in radians or degrees) are congruent. They show the same "openness" between the two rays, line segments or lines that form them.
- Adjacent angles. When two lines cross each other, they form four angles. Any two angles sharing a ray, line segment or line are adjacent. In the following drawing, Line JC intersects Line OK, creating four adjacent pairs and intersecting at Point Y. Can you find them all?
- Vertical angles. In our same drawing above, angles that skip an angle, that is, angles that are not touching each other except at their vertex, are vertical angles.
- Corresponding angles. Anytime a transversal crosses two other lines, we get corresponding angles. The more restrictive our intersecting lines get, the more restrictive are their angle relationships.
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 polygon is an important concept in geometry that is used to describe the angle formed by a line that extends outside the polygon. In this article, we will discuss the definition of an exterior angle, its properties, and how to calculate it. Definition of Exterior Angle
Each exterior angle and corresponding interior angle of a triangle make up a linear pair of angles. Accordingly, the interior and exterior angles add up to \(180^\circ\). The sum of the two opposing internal angles determines the measure of the exterior angle of a triangle. Another name for this characteristic is the exterior angle theorem.
People also ask
What is exterior angle?
What is the difference between interior angles and exterior angles?
What is an exterior angle of a polygon?
How do you calculate exterior angles?
What is the exterior angle of a triangle?
What are the two types of exterior angle relationships?
An exterior angle is defined as the angle that is formed outside the polygon between a side of the polygon and its adjacent extended side. A polygon is a flat shape or figure that is made up of at least three straight sides and three angles. The exterior angle is created between the extended line and one adjacent side of the polygon.
