ANGLE ADDITION POSTULATE

The angle addition postulate states that if D is in the interior of ∠ABC, then

∠ABD + ∠DBC  =  ∠ABC

60° + 40°  =  100°

Problem 1 : 

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

Solution :

By Angle Addition Postulate, 

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 :

By Angle Addition Postulate, 

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 :

By Angle Addition Postulate, 

m∠EDW + m∠WDC  =  m∠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 :

By Angle Addition Postulate, 

m∠IHQ + m∠QHG  =  m∠IHG

m∠IHQ + 130°  =  145°

Subtract 130° from each side. 

m∠IHQ  =  15°

Problem 5 : 

m∠FCD = x° + 41°, if m∠BCF = x° + 78° and m∠BCD = 95°. Find x. 

Solution :

By Angle Addition Postulate, 

m∠BCF + m∠FCD  =  m∠BCD

x° + 41° + x° + 78°  =  95°

Simplify. 

2x + 119  =  95

Subtract 119 from each side. 

2x  =  -24

Divide each side by 2.

x  =  -12

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