Find measures of complementary, supplementary, vertical and adjacent angles

Key notes:

1. Complementary Angles

• Definition: Two angles are complementary if the sum of their measures equals 90 degrees.
• Example: If one angle measures 30 degrees, the other angle must measure 90−30=60 degrees.
• Visualization: Often represented as two angles that form a right angle (90 degrees) when combined.

2. Supplementary Angles

• Definition: Two angles are supplementary if the sum of their measures equals 180 degrees.
• Example: If one angle measures 110 degrees, the other angle must measure 180-110=70 degrees.
• Visualization: Often represented as two angles that form a straight line (180 degrees) when combined.

3. Vertical Angles

• Definition: Vertical angles are the angles opposite each other when two lines intersect. They are always equal in measure.
• Example: If two lines intersect and one angle measures 50 degrees, the angle directly opposite it also measures 50 degrees.
• Visualization: Formed by the “X” shape created by two intersecting lines.

4. Adjacent Angles

• Definition: Adjacent angles are two angles that share a common side and a common vertex but do not overlap.
• Example: In a shape with four angles, if one angle is 45 degrees and shares a side with another angle, they are adjacent.
• Visualization: Often seen in polygons, such as quadrilaterals, where angles are next to each other.