Download review sheet # 5: angles of polygons

Review Sheet # 5
NAME_______________________________________DATE_______________PER._______
REVIEW SHEET # 5: ANGLES OF POLYGONS
PART 1. IMPORTANT GEOMETRIC TERMS
Write a thorough definition for each of the following geometric terms.
A figure formed by the segments determined by 3 non1. ___________________________ collinear points.
A triangle with no two sides congruent.
2. _
Scalene Triangle_________
A triangle with at least two sides congruent.
3. ___________________________
A triangle with all sides congruent.
4. ____Equilateral Triangle______
A triangle in which all of the angles are acute.
5. ___________________________
A triangle with an obtuse angle.
6. ____Obtuse Triangle______
A triangle with a right angle.
7. ___________________________
A triangle with all angles congruent.
8. ___________________________
9. ______Polygon_____________
A closed figure formed by three or more segments
intersecting at their endpoints.
PART 2. TRIANGLE BASICS
Decide if the following lengths can be sides of a triangle. If yes, classify the triangles by
SIDES.
10.
YES
or
NO (18 is NOT bigger than 20)
8, 10, 20
Classification:___none__________________
11.
YES
or
NO
10, 11, 14
Classification:_________________________
12.
YES
or
NO
Classification:_________________________
10, 10, 10
Review Sheet # 5 Pg. 2
The measures of two angles of a triangle are given. Find the measure of the third angle,
then classify the triangle by ANGLES.
13. Third Angle = ___90_________
57, 33
Classification:______Right Triangle________
14. Third Angle = ____________
36, 52
Classification:_________________________
15. Third Angle = ____________
50, 50
Classification:_________________________
Choose the best answer for each of the following.
___D__16. Which of the following CANNOT be the length of the third side?
A.
B.
C.
D.
______17.
4
5
6
7 (3+4 = 7; must be GREATER THAN 7)
3
4
Which of the following CANNOT be the length of the third side.
A.
B.
C.
D.
3
4
5
6
5
PART 3. ANGLES OF TRIANGLES
Find the specified value(s).
18. x = ___69____
2
x + 21 + 90 = 180
x + 111= 180
x
21
19. y = __________
100
y
160
Review Sheet # 5 Pg. 3
ADD UP ALL x’s and set it equal to 180
E
20. x = __________
m  E = __________
2x
x F
D x
ADD THE 2 INSIDE ANGLES AND SET IT EQUAL TO
OUTSIDE ANGLE
B
80
21. x = __________
m  C = _________
m  ABC = __________
A
x
(2x – 4)
C
Answer each of the following.
In ABC, AB = 6, BC = 8, and AC = 12. List the angles of
ABC in order from largest to smallest.
22. Angles:
< B, < A, < C
**DRAW the Triangle**
In XYZ, mX = 103, mY = 41, and mZ = 36. List the
sides of XYZ in order from shortest to longest.
23. Sides:
PART 4. POLYGONS AND THEIR ANGLES
Classify each of the following polygons, then determine if it is convex or concave.
24.
25.
Classification:____________________
CONVEX
or
CONCAVE?
Classification:____________________
CONVEX
or
CONCAVE?
Review Sheet # 5 Pg. 4
Find the following.
___1440_______26.
Find the sum of the measures of the interior angles of a decagon.
180(n- 2)= 180 (10 – 8) = 180 (8) = 1440
_______________27.
Find the sum of the measures of the interior angles of an
undecagon.
_______________28.
Find the measure of one interior angle of a regular undecagon.
____156______29.
Find the measure of one interior angle of a regular polygon with 15
sides.
One interior angle = 180 (n- 2)/ n
= 180 (15- 2)/15
= 180(13)/15
= 2340/15
_______________30.
Find the number of sides of a regular polygon, if each interior angle
has a measure of 162
_______________31.
The sum of the measures of the interior angles of a polygon is 900.
Find the number of sides of the polygon.
Review Sheet #5 Pg. 5
_______________32.
Find the sum of the exterior angles of a 32-gon.
_______________33.
Find the measure of one exterior angle of a regular polygon with 14
sides.
_____16_______34.
Find the number of sides of a regular polygon if each exterior angle
has a measure of 22.5.
n = 360/ exterior angle = 360/22.5 = 16
PART 5. REVIEW
For each of the following pairs of angles, tell what type of pair they are, and tell whether
each pair is congruent or supplementary.
1 2
4 3
6 5
8 7
ANGLE PAIR
35. 1 and 6
36. 2 and 7
37. 5 and 3
38. 4 and 8
39. 1 and 7
TYPE
CORRESPONDING
 or SUPPLEMENTS?
CONGRUENT