Geometry: Types of Angles and Properties

Types of Angles

• Acute Angle: An angle whose measure is between 0° and 90°.
• Right Angle: An angle whose measure is exactly 90°.
• Obtuse Angle: An angle whose measure is between 90° and 180°.
• Straight Angle: An angle whose measure is exactly 180°.
• Reflex Angle: An angle whose measure is between 180° and 360°.

Angle Properties

• Complementary Angles: Two angles whose sum is 90°.
• Supplementary Angles: Two angles whose sum is 180°.
• Adjacent Angles: Two angles that share a common vertex and side.
• Vertical Angles: Two angles formed by two intersecting lines.

Measuring Angles

• Degree: A unit of measurement for angles, where 1 degree is 1/360 of a full circle.
• Minutes and Seconds: Subunits of degrees, where 1 minute is 1/60 of a degree and 1 second is 1/60 of a minute.

Angle Relationships

• Congruent Angles: Two angles that have the same measure.
• Equivalent Angles: Two angles that have the same measure or can be made to have the same measure by adding or subtracting multiples of 360°.
• Alternate Interior Angles: Two angles formed by two lines and a transversal, where one angle is inside the region between the two lines and the other angle is outside the region.

Types of Angles

• Acute angles measure between 0° and 90°.
• Right angles are exactly 90°.
• Obtuse angles measure between 90° and 180°.
• Straight angles are exactly 180°.
• Reflex angles measure between 180° and 360°.

Angle Properties

• Complementary angles add up to 90°.
• Supplementary angles add up to 180°.
• Adjacent angles share a common vertex and side.
• Vertical angles are formed by two intersecting lines.

Measuring Angles

• A degree is a unit of measurement for angles, equal to 1/360 of a full circle.
• Minutes are subunits of degrees, with 1 minute equal to 1/60 of a degree.
• Seconds are subunits of minutes, with 1 second equal to 1/60 of a minute.

Angle Relationships

• Congruent angles have the same measure.
• Equivalent angles have the same measure or can be made equivalent by adding or subtracting multiples of 360°.
• Alternate interior angles are formed by two lines and a transversal, with one angle inside and one angle outside the region between the lines.