FINDING ANGLE MEASURES INVOLVING DIAGONALS OF A RHOMUS WORKSHEET

Find the all numbered angles in the following rhombus.

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

Solution

Problem 8 :

Solution

Problem 9 :

Solution

Problem 10 :

Solution

Answer Key

1)  ∠1 = 53.5, ∠2 = 53.5, ∠3 = 53.5, ∠4 = 53.5

2)  ∠1 = 38, ∠2 = 38, ∠3 = 38, ∠4 = 38

3)  ∠1 = 26, ∠2 = 128, ∠3 = 128

4) ∠1 = 118, ∠2 = 31, ∠3 = 31

5)  ∠1 = 32, ∠2 = 90, ∠3 = 58, ∠4 = 32

6)  ∠1 = 90, ∠2 = 60, ∠3 = 60, ∠4 = 30

7) ∠1 = 55, ∠2 = 35, ∠3 = 55, ∠4 = 90

8) ∠1 = 60, ∠2 = 90, ∠3 = 30

9)  ∠1 = ∠3 = 90, ∠2 = 55

10)  ∠1 = 38, ∠2 = 90, ∠3 = ∠4 = 90

Problem 1 :

For rhombus JMLK, find each angle measure.

1)  ∠1      2)  ∠2      3)  ∠3     4)  ∠4      5)  ∠JML      6)  ∠MLK+

Solution

Problem 2 :

For rhombus JLMK, find each line segment and angle measure.

1)  ∠1      2)  ∠2      3)  ∠3     4)  ∠4      5)  ∠5      6)  LK    7)  MK

Solution

Problem 3 :

For rhombus SLTM, find the missing values. If ∠1 = 3x + 8, ∠2 = 11x - 24, find

1)  x =      2)  ∠1      3)  ∠2     4)  ∠3      5)  ∠4      6)  ∠5

Solution

Problem 4 :

For rhombus SLTM, find the missing values, if ∠1 = 5x and ∠2 = x2 - 50, find 

1)  x =      2)  ∠1      3)  ∠2     4)  ∠3      5)  ∠4      6)  ∠5

Solution

Problem 5 :

Find

1)  ∠D  2)  ∠DCB    3) ∠1    4)  ∠2     5)  ∠3      6)  ∠4

Solution

Problem 6 :

Find all missing angles.

Solution

Problem 7 :

Find the measure of the numbered angles.

Solution

Answer Key

1)  ∠1  =  25, ∠2  =  90, ∠3 = 65, ∠4 = 65, ∠JML = 130, ∠MLK = 50

2) ∠1 = 40, ∠2 = 40, ∠3 = 50, ∠4 = 50, ∠5 = 90, LK = 20, MK = 18.6

3) x = 4,  ∠1  = 20, ∠2 = 20, ∠3 = 70, ∠4  =  70, ∠5 = 90

4) x = 10 and x = -5, ∠1 = 50, ∠2 = 50, ∠3 = 40, ∠4 = 40, ∠5 = 90

5)  ∠D = 130, ∠DCB = 50, ∠1 = ∠2 = ∠3 = ∠4 = 25

6) ∠1 = 72, ∠2 = 54,∠3 = 54, ∠4 = 72

7) ∠1 = 70, ∠2 = 90, ∠3 = 70, ∠4 = 70

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