Angles & Geometry
Identify and calculate complementary, supplementary, and vertically opposite angles, and explore angle relationships formed by parallel lines and transversals.
Types of Angles
Angles are measured in degrees (°). A full rotation is 360°.
Right Angle
= 90°
Acute Angle
< 90°
Obtuse Angle
90° – 180°
Straight Angle
= 180°
Complementary and Supplementary Angles
Complementary Angles
Two angles that add up to 90°. They form a right angle together.
a + b = 90°
e.g. 35° and 55°
Supplementary Angles
Two angles that add up to 180°. They form a straight line together.
a + b = 180°
e.g. 110° and 70°
Memory trick: Complementary = Corner (90°); Supplementary = Straight (180°).
Vertically Opposite Angles
When two straight lines intersect, they form four angles. The angles across from each other (vertically opposite) are always equal.
a = a — vertically opposite angles are equal
b = b — vertically opposite angles are equal
Also: a + b = 180° (angles on a straight line)
Example: if a = 65°, then b = 180° − 65° = 115°
Parallel Lines and Transversals
When a transversal (a line that crosses two parallel lines) creates angles, specific relationships always hold.
Alternate Angles
Equal — on opposite sides of the transversal (Z-shape)
Co-interior Angles
Add to 180° — same side of transversal (C-shape)
Corresponding Angles
Equal — same position at each parallel line (F-shape)
Key Vocabulary
Complementary
Two angles that add to 90°. Think: C for Corner.
Supplementary
Two angles that add to 180°. Think: S for Straight line.
Vertically Opposite
Angles formed across from each other when two lines cross. They are always equal.
Transversal
A line that crosses two or more other lines, creating pairs of angles with special properties.
Worked Examples
Find the complement of 38°.
Complementary angles add to 90°.
Complement = 90° − 38° = 52°
Two lines intersect. One angle is 72°. Find the vertically opposite angle and the adjacent angle.
Vertically opposite: Equal to 72° (vertically opposite angles are equal).
Adjacent angle: 180° − 72° = 108° (angles on a straight line sum to 180°).
Answer: 72° and 108°
A transversal crosses two parallel lines, forming a co-interior angle of 65°. Find the other co-interior angle.
Co-interior angles add to 180°.
Other angle = 180° − 65° = 115°
Knowledge Check
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Key Concepts Summary
- ●Complementary angles add to 90°; supplementary angles add to 180°.
- ●Vertically opposite angles are always equal when two lines intersect.
- ●Alternate angles are equal (Z-shape); corresponding angles are equal (F-shape).
- ●Co-interior angles add to 180° (C-shape) when lines are parallel.
- ●Angles on a straight line add to 180°; angles at a point add to 360°.