Grade 7 Mathematics
Angles have special relationships based on their positions. Understanding these relationships helps us find MISSING ANGLES without measuring!
Key relationships: Complementary (sum to 90), Supplementary (sum to 180), Vertical (equal), Adjacent (share vertex and side)
Two angles that add up to 90 degrees
Think: C = Corner (90)
Two angles that add up to 180 degrees
Think: S = Straight (180)
Opposite angles formed by intersecting lines. They are EQUAL
Think: Across from each other
Angles that share a vertex AND a side
Think: Next-door neighbors
Find the missing angle:
Complementary
35 + x = 90
x = 90 - 35
x = 55 degrees
Supplementary
125 + y = 180
y = 180 - 125
y = 55 degrees
Identify the relationship: Are the angles complementary (add to 90) or supplementary (add to 180)?
Write the equation: Angle 1 + Angle 2 = Total (either 90 or 180)
Solve for the unknown: Subtract the known angle from the total
When two lines intersect, they form 4 angles:
Vertical angles (across from each other) are EQUAL!
Adjacent angles (next to each other) are SUPPLEMENTARY!
If angle a = 70 degrees, then:
The opposite angle a = 70 degrees (vertical angles are equal)
Angle b = 180 - 70 = 110 degrees (supplementary to a)
Special Angle Pairs (when lines are parallel):
Same position at each intersection
EQUAL
Ex: 1 & 5, 2 & 6, 3 & 7, 4 & 8
Between lines, opposite sides
EQUAL
Ex: 3 & 5, 4 & 6
Outside lines, opposite sides
EQUAL
Ex: 1 & 7, 2 & 8
Between lines, same side
SUPPLEMENTARY
Ex: 3 & 6, 4 & 5
WRONG: Guessing that all angle pairs formed by parallel lines are equal.
RIGHT: Most pairs are EQUAL (corresponding, alternate interior, alternate exterior), but SAME-SIDE INTERIOR angles are SUPPLEMENTARY (add to 180)!
1. Two angles are complementary. One angle is 42 degrees. Find the other angle.
Equation: 42 + x =
Missing angle: degrees
2. Two angles are supplementary. One angle is 98 degrees. Find the other angle.
Equation: 98 + x =
Missing angle: degrees
3. Two lines intersect. One angle measures 75 degrees. Find all four angles.
Vertical angle (opposite): degrees
Adjacent angles: degrees and degrees
4. Parallel lines are cut by a transversal. If angle 1 = 65 degrees, find:
Corresponding angle (angle 5): degrees
Alternate interior angle (angle 4 to angle 6): angle 6 = degrees
Same-side interior angles: angle 3 + angle 6 = degrees