Angle
An angle is formed by two rays or two line segments that have a common endpoint called the vertex.
An interior angle is an angle formed inside a polygon by two adjacent sides.
An exterior angle of a polygon is an angle formed outside the polygon by extending one of its sides.
Congruent angles are angles that have the same measure.
The angle measure axiom states that the measure of an angle is a unique number between 0 and 360 degrees.
Types of Angles
- Right Angle
- Acute Angle
- Obtuse Angle
- Straight Angle
- Reflex Angle
- Complementary Angles
- Supplementary Angles
- Angle Bisector
- Adjacent Angles
- Linear Pair of Angles
- Vertically Opposite Angles
- Transversal
- Corresponding Angles
- Alternate Interior Angles
- Consecutive Interior Angles
Right Angle
An angle that measures exactly 90 degrees.
Example: The angle formed between the hour and minute hand at 3 o'clock.
Acute Angle
An angle that measures less than 90 degrees.
Example: The angle formed by two hands of a clock at 1 o'clock.
Obtuse Angle
An angle that measures more than 90 degrees but less than 180 degrees.
Example: The angle formed by two hands of a clock at 10 o'clock.
Straight Angle
An angle that measures exactly 180 degrees.
Example: The angle formed by a straight line on a sheet of paper.
Reflex Angle
An angle that measures more than 180 degrees but less than 360 degrees.
Example: The angle formed by the minute hand of a clock at 10 o'clock.
Complementary Angles
Two angles whose sum is 90 degrees.
Example: An angle of 30 degrees and an angle of 60 degrees are complementary.
Supplementary Angles
Two angles whose sum is 180 degrees.
Example: An angle of 120 degrees and an angle of 60 degrees are supplementary.
Angle Bisector
A line or ray that divides an angle into two equal parts.
Example: The bisector of a 90-degree angle divides it into two 45-degree angles.
Adjacent Angles
Two angles that share a common vertex and a common side but do not overlap.
Example: In a rectangle, adjacent angles are formed at each vertex.
Linear Pair of Angles
Two adjacent angles that form a straight line, totaling 180 degrees.
Example: Angles at the ends of a straight line, such as angles in a straight angle.
Vertically Opposite Angles
Angles that are opposite each other when two lines intersect; they are equal in measure.
Example: The angles formed by the intersection of two straight lines.
Transversal
A line that intersects two or more other lines at distinct points.
Example: A line intersecting two parallel lines forms corresponding angles.
Corresponding Angles
Angles that occupy the same relative position at each intersection where a straight line crosses two others.
Example: Angles formed when a transversal crosses two parallel lines.
Alternate Interior Angles
Angles that are on opposite sides of the transversal and inside the two lines, but on different lines.
Example: Angles formed on the inside of two lines when a transversal crosses them.
Consecutive Interior Angles
Angles that are on the same side of the transversal and inside the two lines, but on different lines.
Example: Angles formed on the inside of two lines when a transversal crosses them.
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