Geometry worksheet for finding missing angle measures using angle relationships.

I'll solve this step by step, finding each missing angle measure.

Problem 1: m∠1 = ?
- We have a right angle (90°) split into two angles: ∠1 and a 32° angle
- So: m∠1 + 32° = 90°
- m∠1 = 90° - 32° = 58°

Problem 2: m∠JMK = ?
- We have a straight line (180°) with three angles: 47°, JMK, and 56°
- So: 47° + m∠JMK + 56° = 180°
- 103° + mJMK = 180°
- m∠JMK = 180° - 103° = 77°

Problem 3: m∠ONP = ?
- Given: m∠MNO = 130°
- MNO and ∠ONP form a straight line (180°)
- So: 130° + m∠ONP = 180°
- m∠ONP = 180° - 130° = 50°

Problem 4: m∠2 = ?
- We have a straight line (180°) with two angles: 145° and ∠2
- So: 145° + m∠2 = 180°
- m∠2 = 180° - 145° = 35°

Problem 5: m∠AED = ?
- We have a straight line with angles: ∠AEB, BEC, and ∠CED
- Given: m∠AEB = 38°, m∠BEC = 54°
- These three angles form a straight line (180°)
- So: 38° + 54° + m∠CED = 180°
- 92° + m∠CED = 180°
- m∠CED = 180° - 92° = 88°
- But we need m∠AED = m∠AEB + m∠BEC + m∠CED = 38° + 54° + 88° = 180°

Wait, let me reconsider. Looking at the diagram more carefully, ∠AED appears to be the angle from A to D passing through E. Let me recalculate:
- m∠AED = m∠AEB + m∠BEC + m∠CED
- We know m∠AEB = 38°, m∠BEC = 54°
- The remaining angle to complete 180° is m∠CED = 180° - 38° - 54° = 88°
- Therefore m∠AED = 38° + 54° + 88° = 180°

Actually, I think ∠AED might just be asking for one specific angle. Let me look at the pattern - it seems like these are individual angles. If ∠AED is the angle between rays EA and ED, and we have the full straight line broken into parts, then mAED would be the sum of all angles on that side. But given the answer format, I believe m∠AED = 88° (the remaining angle).

Let me reconsider the diagram structure. If A-E-D forms a straight line and B and C are points creating angles, then:
- m∠AED would be the angle not including B and C
- Actually, looking at typical problems like this, m∠AED likely refers to ∠CED = 88°

Problem 6: m∠MEG = ?
- We have angles around point E
- Given: m∠FEG = 42°, m∠DEF = 35°
- These appear to be adjacent angles
- m∠MEG would be the remaining angle to complete some relationship
- Without seeing the exact diagram clearly, if M-E-G forms a straight line with F in between:
- m∠MEG = 180° - 42° - 35° = 103°

Problem 7: m∠AGT = ?
- We have a straight line AGT with ray GB
- Given: m∠BGT = 55°
- ∠AGT and ∠BGT form a straight line
- m∠AGT = 180° - 55° = 125°

Problem 8: m∠KIN = ?
- We have angles around point I
- Given: m∠HIK = 63°, m∠JIH = 49°
- If H-I-N forms a straight line:
- m∠KIN = 180° - 63° - 49° = 68°

Problem 9: m∠LTO = ?
- We have a straight line with angles
- Given: m∠MTL = 128°
- LTO and ∠MTL form a straight line
- m∠LTO = 180° - 128° = 52°

Problem 10: m∠J = ?
- We have a triangle or angles around a point
- Given: m∠K = 58°, mL = 47°
- If these are angles in a triangle:
- m∠J + 58° + 47° = 180°
- m∠J + 105° = 180°
- m∠J = 180° - 105° = 75°

Final Answer:
1. m∠1 = 58°
2. m∠JMK = 77°
3. m∠ONP = 50°
4. m2 = 35°
5. mAED = 88°
6. m∠MEG = 103°
7. m∠AGT = 125°
8. m∠KIN = 68°
9. m∠LTO = 52°
10. m∠J = 75°