Let’s solve each problem using the
angle addition postulate. This means:
If two angles are next to each other and share a side, their measures add up to make the bigger angle that contains them.
We’ll go one by one.
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Problem 1)
Given:
∠DEG = 66°
∠DEF = 140°
Find ∠GEF
Since ∠DEG + ∠GEF = ∠DEF (they’re adjacent and form the big angle),
→ 66° + ∠GEF = 140°
→ ∠GEF = 140° - 66° =
74°
✔ Answer:
74°
---
Problem 2)
Given:
∠BCE = 77°
∠ECD = 58°
Find ∠BCD
These two angles are next to each other and together make ∠BCD.
→ ∠BCD = 77° + 58° =
135°
✔ Answer:
135°
---
Problem 3)
Given:
∠GHK = 71°
∠KHJ = 19°
Find ∠GHJ
They are adjacent — so add them:
→ ∠GHJ = 71° + 19° =
90°
✔ Answer:
90°
---
Problem 4)
Given:
∠DBC = 65°
∠ABC = 130°
Find ∠ABD
∠ABD + ∠DBC = ∠ABC
→ ∠ABD + 65° = 130°
→ ∠ABD = 130° - 65° =
65°
✔ Answer:
65°
---
Problem 5)
Given:
∠LJK = 17°
∠HJK = 100°
Find ∠HJL
∠HJL + ∠LJK = ∠HJK
→ ∠HJL + 17° = 100°
→ ∠HJL = 100° - 17° =
83°
✔ Answer:
83°
---
Problem 6)
Given:
∠OPR = 84°
∠RPQ = 26°
Find ∠OPQ
Add them:
→ ∠OPQ = 84° + 26° =
110°
✔ Answer:
110°
---
Problem 7)
Given:
∠PQS = 113°
∠PQR = 160°
Find ∠SQR
∠PQS + ∠SQR = ∠PQR
→ 113° + ∠SQR = 160°
→ ∠SQR = 160° - 113° =
47°
✔ Answer:
47°
---
Problem 8)
Given:
∠QRT = 92°
∠QRS = 126°
Find ∠TRS
∠QRT + ∠TRS = ∠QRS
→ 92° + ∠TRS = 126°
→ ∠TRS = 126° - 92° =
34°
✔ Answer:
34°
---
Problem 9)
Given:
∠EFH = 110°
∠HFG = 35°
Find ∠EFG
Add them:
→ ∠EFG = 110° + 35° =
145°
✔ Answer:
145°
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Final Answer:
1) 74°
2) 135°
3) 90°
4) 65°
5) 83°
6) 110°
7) 47°
8) 34°
9) 145°
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting angles worksheet.
