Question

the angle addition postulate

1. find m∠klm if m∠klb = 26° and m∠blm = 60°.
2. find m∠fgh if m∠fgb = 105° and m∠bgh = 54°.
3. m∠ghc = 60° and m∠chi = 104°. find m∠ghi.
4. find m∠wvu if m∠zvu = 62° and m∠wvz = 50°.
5. m∠fmn = 99° and m∠lmf = 36°. find m∠lmn.
6. find m∠wdc if m∠edc = 145° and m∠edw = 61°.
7. find m∠jkl if m∠skl = 31° and m∠jks = 52°.
8. find m∠ihq if m∠ihg = 176° and m∠qhg = 130°.
9. find m∠klu if m∠ulm = 20° and m∠klm = 110°.
10. find m∠ija if m∠ajk = 61° and m∠ijk = 153°.

Explanation:

Step1: Recall angle - addition postulate

The measure of the whole angle is the sum of the measures of its non - overlapping parts.

Step2: Solve problem 1

$m\angle KLM=m\angle KLB + m\angle BLM$. Given $m\angle KLB = 26^{\circ}$ and $m\angle BLM = 60^{\circ}$, then $m\angle KLM=26^{\circ}+60^{\circ}=86^{\circ}$.

Step3: Solve problem 2

$m\angle FGH=m\angle FGB + m\angle BGH$. Given $m\angle FGB = 105^{\circ}$ and $m\angle BGH = 54^{\circ}$, then $m\angle FGH=105^{\circ}+54^{\circ}=159^{\circ}$.

Step4: Solve problem 3

$m\angle GHI=m\angle GHC + m\angle CHI$. Given $m\angle GHC = 60^{\circ}$ and $m\angle CHI = 104^{\circ}$, then $m\angle GHI=60^{\circ}+104^{\circ}=164^{\circ}$.

Step5: Solve problem 4

$m\angle WVU=m\angle WVZ + m\angle ZVU$. Given $m\angle ZVU = 62^{\circ}$ and $m\angle WVZ = 50^{\circ}$, then $m\angle WVU=50^{\circ}+62^{\circ}=112^{\circ}$.

Step6: Solve problem 5

$m\angle LMN=m\angle LMF + m\angle FMN$. Given $m\angle LMF = 36^{\circ}$ and $m\angle FMN = 99^{\circ}$, then $m\angle LMN=36^{\circ}+99^{\circ}=135^{\circ}$.

Step7: Solve problem 6

$m\angle WDC=m\angle EDC - m\angle EDW$. Given $m\angle EDC = 145^{\circ}$ and $m\angle EDW = 61^{\circ}$, then $m\angle WDC=145^{\circ}-61^{\circ}=84^{\circ}$.

Step8: Solve problem 7

$m\angle JKL=m\angle JKS + m\angle SKL$. Given $m\angle JKS = 52^{\circ}$ and $m\angle SKL = 31^{\circ}$, then $m\angle JKL=52^{\circ}+31^{\circ}=83^{\circ}$.

Step9: Solve problem 8

$m\angle IHQ=m\angle IHG - m\angle QHG$. Given $m\angle IHG = 176^{\circ}$ and $m\angle QHG = 130^{\circ}$, then $m\angle IHQ=176^{\circ}-130^{\circ}=46^{\circ}$.

Step10: Solve problem 9

$m\angle KLU=m\angle KLM - m\angle ULM$. Given $m\angle KLM = 110^{\circ}$ and $m\angle ULM = 20^{\circ}$, then $m\angle KLU=110^{\circ}-20^{\circ}=90^{\circ}$.

Step11: Solve problem 10

$m\angle IJA=m\angle IJK - m\angle AJK$. Given $m\angle IJK = 153^{\circ}$ and $m\angle AJK = 61^{\circ}$, then $m\angle IJA=153^{\circ}-61^{\circ}=92^{\circ}$.

Answer:

1. $m\angle KLM = 86^{\circ}$
2. $m\angle FGH = 159^{\circ}$
3. $m\angle GHI = 164^{\circ}$
4. $m\angle WVU = 112^{\circ}$
5. $m\angle LMN = 135^{\circ}$
6. $m\angle WDC = 84^{\circ}$
7. $m\angle JKL = 83^{\circ}$
8. $m\angle IHQ = 46^{\circ}$
9. $m\angle KLU = 90^{\circ}$
10. $m\angle IJA = 92^{\circ}$