Review Sheet # 5: Angles of Polygons

Review Sheet # 5: Angles of Polygons

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.

  1. ______
/ A figure formed by the segments determined by 3 non-collinear points.
  1. _ Scalene Triangle______
/ A triangle with no two sides congruent.
  1. ______
/ A triangle with at least two sides congruent.
  1. ____Equilateral Triangle______
/ A triangle with all sides congruent.
  1. ______
/ A triangle in which all of the angles are acute.
  1. ____Obtuse Triangle______
/ A triangle with an obtuse angle.
  1. ______
/ A triangle with a right angle.
  1. ______
/ A triangle with all angles congruent.
  1. ______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.

  1. YES or NO (18 is NOT bigger than 20)
Classification:___none______/ 8, 10, 20
  1. YES or NO
Classification:______/ 10, 11, 14
  1. YES or NO
Classification:______/ 10, 10, 10

The measures of two angles of a triangle are given. Find the measure of the third angle, then classify the triangle by ANGLES.


  1. Third Angle = ___90______
Classification:______Right Triangle______/ 57, 33
  1. Third Angle = ______
Classification:______/ 36, 52
  1. Third Angle = ______
Classification:______/ 50, 50

Choose the best answer for each of the following.

___D__16. / Which of the following CANNOT be the length of the third side?

  1. 4
  2. 5
  3. 6
  4. 7 (3+4 = 7; must be GREATER THAN 7)


______17. / Which of the following CANNOT be the length of the third side.
  1. 3
  2. 4
  3. 5
  4. 6

PART 3. ANGLES OF TRIANGLES

Find the specified value(s).

18. x = ___69____ / x + 21 + 90 = 180
x + 111= 180

19. y = ______

20. x = ______
mE = ______/ ADD UP ALL x’s and set it equal to 180

21. x = ______
mC = ______
mABC = ______/ ADD THE 2 INSIDE ANGLES AND SET IT EQUAL TO OUTSIDE ANGLE

Answer each of the following.

22. Angles:
< B, < A, < C
**DRAW the Triangle** / In ABC, AB = 6, BC = 8, and AC = 12. List the angles of ABC in order from largest to smallest.
23. Sides: / In XYZ, mX = 103, mY = 41, and mZ = 36. List the sides of XYZ in order from shortest to longest.

PART 4. POLYGONS AND THEIR ANGLES

Classify each of the following polygons, then determine if it is convex or concave.


24.
Classification:______

CONVEX or CONCAVE?

/ 25.
Classification:______

CONVEX or CONCAVE?

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.
______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.

ANGLE PAIR

/ TYPE /  or SUPPLEMENTS?
  1. 1 and 6
/ CORRESPONDING / CONGRUENT
  1. 2 and 7

  1. 5 and 3

  1. 4 and 8

  1. 1 and 7

Top View