Angles in 4 or 5 Sided Figures
CONCEPTS
n-Sided Figures (Polygons)
• S = 180° * (n-2) (n = number of sides, S = angle)
• Sum of angles in a 4-sided figure = 360°. Sum of angles in a 5-sided figure = 540°
• Potentially break up a figure into 2 triangles to determine the angles
Parallelograms
• Opposite angles are equal
• Diagonals do not have equal angles on either side of the diagonal (parallelograms only)
• The sum of angles in a 4 sided figure is 360°
Trapezoids
• Angled sides have equal lengths
• The top and bottom of the figure are parallel
• The sum of angles in a 4 sided figure is 360°
Pentagons
• The sum of angles in a 5 sided figure is 540°
PRACTICE PROBLEMS
Question 1 Given the equation for n-Sided Figures, what is the sum of angles in a figure with 7 sides?
-- Answer -- 900°
S = 180° * (n - 2) = 180° * (9 - 2) = 180° * 7 = 900°
Question 2 What is the measure of ∠ A (see figure below)?
-- Answer -- 83°
∠B = 40° = ∠D = 40°
∠A = 180° - 57° - 40° = 83°
Question 3 What is ∠ A if ∠ C is 80° and ∠ B is 60° (see figure below)?
-- Answer -- 140°
360° - (2 * 80°) - 60° = 140°
Question 4 What is the angle of ∠ DBC for the isosceles trapezoid (see figure below)?
TIP: Isosceles trapezoids have equal sides.
-- Answer -- 95°
Question 5 The measure of the angles of a 5 sided figure are 100°, 89°, 87°, and 110°. What is the measure of the 5th angle?
-- Answer -- 154°
540° = 100° + 89° + 87° + 110° + x
x = 154°
ACT PRACTICE PROBLEMS
