Download 6-1 Angles of Polygons 12-17

12/18/2015
Five-Minute Check (over Chapter 5)
CCSS
Then/Now
New Vocabulary
Theorem 6.1: Polygon Interior Angles Sum
Example 1: Find the Interior Angles Sum of a Polygon
Example 2: Real-World Example: Interior Angle Measure of
Regular Polygon
Example 3: Find Number of Sides Given Interior Angle
Measure
Theorem 6.2: Polygon Exterior Angles Sum
Example 4: Find Exterior Angle Measures of a Polygon
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Over Chapter 5
State whether this sentence is always, sometimes,
or never true. The three altitudes of a triangle
intersect at a point inside the triangle.
Find n and list the sides of ∆PQR in order from
shortest to longest if m∠
∠P = 12n – 15,
m∠
∠Q = 7n + 26, and m∠R = 8n – 47.
State the assumption you would make to start an
indirect proof of the statement.
If –2x ≥ 18, then x ≤ –9.
Find the range for the measure of the third side of
a triangle given that the measures of two sides
are 43 and 29.
Over Chapter 5
State whether this sentence is always, sometimes,
or never true. The three altitudes of a triangle
intersect at a point inside the triangle.
A. always
B. sometimes
C. never
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Over Chapter 5
Find n and list the sides of ∆PQR in order from
shortest to longest if m∠
∠P = 12n – 15,
m∠
∠Q = 7n + 26, and m∠R = 8n – 47.
A. n = 8;
B. n = 8;
C. n = 6;
D. n = 6;
Over Chapter 5
State the assumption you would make to start an
indirect proof of the statement.
If –2x ≥ 18, then x ≤ –9.
A. x is positive.
B. –2x < 18
C. x > –9
D. x < 9
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Over Chapter 5
Find the range for the measure of the third side of
a triangle given that the measures of two sides
are 43 and 29.
A. n > 14
B. 14 < n < 72
C. 29 < n < 43
D. n > 0
Content Standards
G.MG.1 Use geometric shapes, their
measures, and their properties to describe
objects (e.g., modeling a tree trunk or a
human torso as a cylinder).
Mathematical Practices
4 Model with mathematics.
3 Construct viable arguments and critique
the reasoning of others.
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You named and classified polygons.
• Find and use the sum of the measures of the
interior angles of a polygon.
• Find and use the sum of the measures of the
exterior angles of a polygon.
• diagonal
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Find the Interior Angles Sum of a Polygon
A. Find the sum of the measures of the interior
angles of a convex nonagon.
“nonagon” → 9 sides
Sum of the interior angles = (n – 2)180
(n – 2) ● 180 = (9 – 2) ● 180
= 7 ● 180 or 1260
Answer: The sum of the measures is 1260.
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Find the Interior Angles Sum of a Polygon
B. Find the measure of each interior angle of
parallelogram RSTU.
Step 1 Find x.
Recall: sum of interior angles = 180(n – 2)
∠ + ∠ + ∠ + ∠ = 180(n – 2)
5x + (11x + 4) + 5x + (11x + 4) = 180(4 – 2)
5x + 11x + 4 + 5x + 11x + 4 = 180(2)
32x + 8 = 360
32x = 352
x = 11
Find the Interior Angles Sum of a Polygon
B. Find the measure of each interior angle of
parallelogram RSTU.
Step 2 Find the measure of each angle
∠ = ∠ = 11x + 4
∠ = ∠ = 5x
∠ = ∠ = 5(11) ∠ = ∠ = 11(11) + 4
∠ = ∠ = 121 + 4
∠ = ∠ = 55
∠ = ∠ = 125
Answer: m∠R = 55, m∠S = 125, m∠T = 55,
x = 11
m∠U = 125
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A. Find the sum of the measures of the interior
angles of a convex octagon.
A. 900
B. 1080
C. 1260
D. 1440
B. Find the value of x.
A. x = 7.8
B. x = 22.2
C. x = 15
D. x = 10
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The measure of an interior angle of a regular
polygon is 144. Find the number of sides in the
polygon.
A. 12
B. 9
C. 11
D. 10
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Find Exterior Angle Measures of a Polygon
A. Find the value of x in the diagram.
5x + (4x – 6) + (5x – 5) + (4x + 3) + (6x – 12) + (2x + 3) + (5x + 5) = 360
(5x + 4x + 5x + 4x + 6x + 2x + 5x) + [(–6) + (–5) + 3 + (–12) + 3 + 5] = 360
31x – 12 = 360
31x = 372
x = 12
Answer:
x = 12
Find Exterior Angle Measures of a Polygon
B. Find the measure of each exterior angle of a
regular decagon.
“regular decagon” → 10 congruent angles and sides
10n = 360
n = 36
Answer:
The measure of each exterior angle of a
regular decagon is 36.
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A. Find the value of x in
the diagram.
A. 10
B. 12
C. 14
D. 15
B. Find the measure of each exterior angle of a
regular pentagon.
A. 72
B. 60
C. 45
D. 90
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