Problem 1 :

Find m∠KLM, if m∠KLB  =  26° and m∠BLM  =  60°. Problem 2 :

Find m∠FGH, if m∠FGB  =  105° and m∠BGH  =  54°. Problem 3 :

Find m∠WDC, if m∠EDC  =  145° and m∠EDW  =  61°. Problem 4 :

Find m∠IHQ, if m∠IHG  =  176° and m∠QHG  =  130°. Problem 5 :

In the diagram shown below,

m∠FCD  =  x° + 41°

if m∠BCF  =  x° + 78°

m∠BCD  =  95°

Find x. Problem 6 :

In the diagram shown below,

m∠BJK  =  146° + 2x°

m∠IJK  =  172°

m∠IJB  =  2x° + 26°

Find x. Problem 7 :

In the diagram shown below,

m∠GFZ  =  38°

m∠ZFE  =  2x° + 122°

m∠GFE  =  x° + 163°

Find x. Problem 8 :

In the diagram shown below,

m∠LMN  =  135°

m∠LMV  =  -1° + 45x°

m∠VMN  =  23x°

Find x.  ## Solutions

Problem 1 :

Find m∠KLM, if m∠KLB  =  26° and m∠BLM  =  60°. Solution :

m∠KLB + m∠BLM  =  m∠KLM

26° + 60°  =  m∠KLM

86°  =  m∠KLM

Problem 2 :

Find m∠FGH, if m∠FGB  =  105° and m∠BGH  =  54°. Solution :

m∠FGB + m∠BGH  = m∠FGH

105° + 54°  =  m∠KLM

159°  =  m∠KLM

Problem 3 :

Find m∠WDC, if m∠EDC  =  145° and m∠EDW  =  61°. Solution :

m∠EDW + m∠WDC  =  ∠EDC

61° + m∠WDC  =  145°

Subtract 61° from each side.

m∠WDC  =  84°

Problem 4 :

Find m∠IHQ, if m∠IHG  =  176° and m∠QHG  =  130°. Solution :

m∠IHQ + m∠QHG  =  m∠IHG

m∠IHQ + 130°  =  145°

Subtract 130° from each side.

m∠IHQ  =  15°

Problem 5 :

In the diagram shown below,

m∠FCD  =  x° + 41°

if m∠BCF  =  x° + 78°

m∠BCD  =  95°

Find x. Solution :

m∠BCF + m∠FCD  =  ∠BCD

x° + 41° + x° + 78°  =  95°

Simplify.

2x + 119  =  95

Subtract 119 from each side.

2x  =  -24

Divide each side by 2.

x  =  -12

Problem 6 :

In the diagram shown below,

m∠BJK  =  146° + 2x°

m∠IJK  =  172°

m∠IJB  =  2x° + 26°

Find x. Solution :

m∠IJB + m∠BJK  =  m∠IJK

146° + 2x° + 2x° + 26°  =  172°

Simplify.

4x + 172  =  172

Subtract 172 from each side.

4x  =  0

Divide each side by 4.

x  =  0

Problem 7 :

In the diagram shown below,

m∠GFZ  =  38°

m∠ZFE  =  2x° + 122°

m∠GFE  =  x° + 163°

Find x. Solution :

m∠GFZ + m∠ZFE  =  m∠GFE

38° + 2x° + 122°  =  x° + 163°

Simplify.

2x + 160  =  x + 163

x  =  3

Problem 8 :

In the diagram shown below,

m∠LMN  =  135°

m∠LMV  =  -1° + 45x°

m∠VMN  =  23x°

Find x. Solution :

m∠LMV + m∠VMN  =  m∠LMN

-1° + 45x° + 23x°  =  135°

Simplify.

-1 + 68x  =  135

68x  =  136

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