Find missing angles using the angle addition postulate in this math worksheet.

Let’s solve each problem using the angle addition postulate.
This means: if two angles are next to each other and share a side, you can add them together to get the bigger angle.

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 make up the big angle),
→ 66° + ∠GEF = 140°
→ ∠GEF = 140° - 66° = 74°

✔ Answer: 74°

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Problem 2)
Given:
∠BCE = 77°
∠ECD = 58°
Find ∠BCD

These two angles are next to each other → just add them!
→ ∠BCD = 77° + 58° = 135°

✔ Answer: 135°

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Problem 3)
Given:
∠GHK = 71°
∠KHJ = 19°
Find ∠GHJ

Again, they’re adjacent → add them!
→ ∠GHJ = 71° + 19° = 90°

✔ Answer: 90°

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Problem 4)
Given:
∠DBC = 65°
∠ABC = 130°
Find ∠ABD

∠ABD + ∠DBC = ∠ABC
→ ∠ABD + 65° = 130°
→ ∠ABD = 130° - 65° = 65°

✔ Answer: 65°

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Problem 5)
Given:
∠LJK = 17°
∠HJK = 100°
Find ∠HJL

∠HJL + ∠LJK = ∠HJK
→ ∠HJL + 17° = 100°
→ ∠HJL = 100° - 17° = 83°

✔ Answer: 83°

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Problem 6)
Given:
∠OPR = 84°
∠RPQ = 26°
Find ∠OPQ

Add them:
→ ∠OPQ = 84° + 26° = 110°

✔ Answer: 110°

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Problem 7)
Given:
∠PQS = 113°
∠PQR = 160°
Find ∠SQR

∠PQS + ∠SQR = ∠PQR
→ 113° + ∠SQR = 160°
→ ∠SQR = 160° - 113° = 47°

✔ Answer: 47°

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Problem 8)
Given:
∠QRT = 92°
∠QRS = 126°
Find ∠TRS

∠QRT + ∠TRS = ∠QRS
→ 92° + ∠TRS = 126°
→ ∠TRS = 126° - 92° = 34°

✔ Answer: 34°

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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°