Geometry Worksheets | Angles Worksheets - Free Printable

To find the missing angle measurements, we use the Angle Addition Postulate. This rule says that if you have two smaller angles sitting side-by-side to make a larger angle, you can find the total by adding the two small angles together.

The formula is:
Small Angle 1 + Small Angle 2 = Big Angle

Let's solve each problem one by one.

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Problem 1

* Given: $\angle DEG = 66^\circ$, $\angle DEF = 140^\circ$
* Find: $\angle GEF$
* Logic: $\angle DEG$ and $\angle GEF$ combine to make the big angle $\angle DEF$.
* Equation: $66^\circ + \angle GEF = 140^\circ$
* Calculation: $140 - 66 = 74$
* Answer: $74^\circ$

Problem 2

* Given: $\angle BCE = 77^\circ$, $\angle ECD = 58^\circ$
* Find: $\angle BCD$
* Logic: The two smaller angles add up to the big angle $\angle BCD$.
* Equation: $77^\circ + 58^\circ = \angle BCD$
* Calculation: $77 + 58 = 135$
* Answer: $135^\circ$

Problem 3

* Given: $\angle GHK = 71^\circ$, $\angle KHJ = 19^\circ$
* Find: $\angle GHJ$
* Logic: Add the two small angles to get the total angle $\angle GHJ$.
* Equation: $71^\circ + 19^\circ = \angle GHJ$
* Calculation: $71 + 19 = 90$
* Answer: $90^\circ$

Problem 4

* Given: $\angle DBC = 65^\circ$, $\angle ABC = 130^\circ$
* Find: $\angle ABD$
* Logic: $\angle ABD$ and $\angle DBC$ make the big angle $\angle ABC$.
* Equation: $\angle ABD + 65^\circ = 130^\circ$
* Calculation: $130 - 65 = 65$
* Answer: $65^\circ$

Problem 5

* Given: $\angle LJK = 12^\circ$, $\angle HJK = 100^\circ$
* Find: $\angle HJL$
* Logic: $\angle HJL$ and $\angle LJK$ make the big angle $\angle HJK$.
* Equation: $\angle HJL + 12^\circ = 100^\circ$
* Calculation: $100 - 12 = 88$
* Answer: $88^\circ$

Problem 6

* Given: $\angle QPR = 84^\circ$, $\angle RPQ = 26^\circ$ (Note: There is a typo in the worksheet here. $\angle QPR$ and $\angle RPQ$ are actually the same angle. Based on the diagram, the middle angle is $\angle RPQ = 26^\circ$, and the top part is $\angle QPR = 84^\circ$. The big angle is $\angle OPQ$. Let's assume the top part is $84^\circ$ and the bottom part is $26^\circ$).
* Find: $\angle OPQ$
* Logic: Add the top angle and the bottom angle.
* Equation: $84^\circ + 26^\circ = \angle OPQ$
* Calculation: $84 + 26 = 110$
* Answer: $110^\circ$

Problem 7

* Given: $\angle PQS = 113^\circ$, $\angle PQR = 150^\circ$
* Find: $\angle SQR$
* Logic: $\angle PQS$ and $\angle SQR$ make the big angle $\angle PQR$.
* Equation: $113^\circ + \angle SQR = 150^\circ$
* Calculation: $150 - 113 = 37$
* Answer: $37^\circ$

Problem 8

* Given: $\angle QRT = 92^\circ$, $\angle QRS = 126^\circ$
* Find: $\angle TRS$
* Logic: $\angle QRT$ and $\angle TRS$ make the big angle $\angle QRS$.
* Equation: $92^\circ + \angle TRS = 126^\circ$
* Calculation: $126 - 92 = 34$
* Answer: $34^\circ$

Problem 9

* Given: $\angle EFH = 110^\circ$, $\angle HFG = 36^\circ$
* Find: $\angle EFG$
* Logic: Add the two small angles to get the big angle $\angle EFG$.
* Equation: $110^\circ + 36^\circ = \angle EFG$
* Calculation: $110 + 36 = 146$
* Answer: $146^\circ$

Final Answer:
1) 74°
2) 135°
3) 90°
4) 65°
5) 88°
6) 110°
7) 37°
8) 34°
9) 146°