The sum of the measure of two adjacent angles is equal to the measure of the angle formed by the non-common sides of the two adjacent angles.

Example :

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

Solution :

m∠KLM = m∠KLB + m∠BLM

= 26° + 60°

m∠KLM = 86°

Problem 1 :

Find m∠FGH if m∠FGB = 105° and m∠BGH = 54°

Solution :

m∠FGH  = m∠FGB + m∠BGH

= 105° + 54°

m∠FGH = 159°

Problem 2 :

m∠GHC = 60° and m∠CHI = 104°. Find m∠GHI

Solution :

m∠GHI  = m∠GHC m∠CHI

= 60° + 104°

m∠GHI = 164°

Problem 3 :

Find m∠WVU if m∠ZVU = 62° and m∠WVZ = 50°.

Solution :

m∠WVU = m∠ZVU m∠WVZ

= 62° + 50°

m∠WVU = 112°

Problem 4 :

m∠FMN = 99° and m∠LMF = 36°. Find m∠LMN

Solution :

m∠LMN = m∠FMN  m∠LMF

= 99° + 36°

m∠LMN = 135°

Problem 5 :

Find m∠WDC if m∠EDC = 145° and m∠EDW = 61°

Solution :

m∠WDC = m∠EDC - m∠EDW

= 145° - 61°

m∠WDC = 84°

Problem 6 :

Find m∠JKL if m∠SKL = 31° and m∠JKS = 52°.

Solution :

m∠JKL = m∠SKL + m∠JKS

= 31° + 52°

m∠JKL = 83°

Problem 7 :

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

Solution :

m∠IHQ = m∠IHG - m∠QHG

= 176° - 130°

m∠IHQ = 46°

Problem 8 :

Find m∠KLU if m∠ULM = 20° and m∠KLM = 110°.

Solution :

m∠KLU = m∠KLM - m∠ULM

= 110° - 20°

m∠KLU = 90°

Problem 9 :

Find m∠IJA if m∠AJK = 61° and m∠IJK = 153°.

Solution :

m∠IJA = m∠IJK - m∠AJK

= 153° - 61°

m∠IJA = 92°

Problem 10 :

m∠HGF = 16x + 4, m∠EGF = 110°, and m∠HGE = 3x + 11. Find x

Solution :

m∠HGF = m∠HGE + m∠EGF

16x + 4 = 3x + 11 + 110

16x + 4 = 3x + 121

16x - 3x = 121 - 4

13x = 117

x = 117/13

x = 9

Problem 11 :

m∠VUT = 175°, m∠VUJ = 17x − 3, and m∠JUT = 17x + 8. Find x

Solution :

m∠VUT = m∠VUJ + m∠JUT

175° = 17x - 3 + 17x + 8

175 = 34x + 5

Subtracting 5 on both sides, we get

175 - 5 = 34x

34x = 170

x = 170/34

x = 5

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