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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 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 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...
The exterior angle theorem states that an exterior angle of a triangle equals the sum of two remote interior angles. Learn the statement, proof, and examples.
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.
The exterior angle of a triangle is the angle that is formed with one side and the adjacent extended side of a triangle. There are 3 exterior angles in a triangle and the sum of the exterior angles of a triangle is always equal to 360°. How to Find the Exterior Angle of Triangle?
Aug 3, 2023 · Angles that are found outside or external to any geometric shape are called exterior angles. They are also sometimes known as external angles or turning angle. An exterior angle is made by extending one of the lines of the shape beyond the point of intersection. Shown below are the interior angles of some common regular polygons.
