5th Grade Geometry - Free Printable

I will solve each of the six problems on this worksheet to find the missing angles. I'll work through them one by one, applying geometric principles.

Problem 1

This problem shows a right angle (90°) divided into three parts: 35°, an unknown angle, and 25°.
- The sum of these three angles must equal 90°.
- So, the missing angle = 90° - 35° - 25° = 30°.

Problem 2

This problem shows a straight line with three angles along it: 40°, an unknown angle, and 65°.
- Angles on a straight line add up to 180°.
- So, the missing angle = 180° - 40° - 65° = 75°.

Problem 3

This is a triangle with two known angles: 99° and 44°.
- The sum of angles in any triangle is always 180°.
- So, the missing angle = 180° - 99° - 44° = 37°.

Problem 4 (Isosceles Triangle)

This is an isosceles triangle with one angle given as 36°.
- In an isosceles triangle, two angles are equal.
- Since only one angle is given, it must be the unique angle (the vertex angle), and the other two base angles are equal.
- Let each of the equal angles be x.
- Then, 36° + x + x = 180°.
- So, 2x = 180° - 36° = 144°.
- Therefore, x = 72°.
- The two missing angles are both 72°.

Problem 5

This problem shows angles around a point.
- The sum of angles around a point is 360°.
- We have two known angles: 125° and 45°.
- So, the missing angle = 360° - 125° - 45° = 190°.

Wait, let me reconsider Problem 5. Looking at the diagram again, there appear to be three angles shown: 125°, 45°, and the missing angle. But 125° + 45° = 170°, so the missing angle would be 360° - 170° = 190°. However, this seems unusually large for a single angle in such a diagram. Let me check if there's another interpretation.

Actually, looking more carefully, the diagram might show only two angles explicitly labeled (125° and 45°) and one unlabeled angle, making three angles total around the point. My calculation stands: 360° - 125° - 45° = 190°.

Problem 6

This problem also shows angles around a point.
- We have three known angles: 162°, 34°, and 104°.
- The sum of angles around a point is 360°.
- So, the missing angle = 360° - 162° - 34° - 104° = 60°.

Let me verify my calculations:
- Problem 1: 90 - 35 - 25 = 30 ✓
- Problem 2: 180 - 40 - 65 = 75 ✓
- Problem 3: 180 - 99 - 44 = 37 ✓
- Problem 4: (180 - 36) / 2 = 72 ✓
- Problem 5: 360 - 125 - 45 = 190 ✓
- Problem 6: 360 - 162 - 34 - 104 = 60 ✓

All calculations appear correct based on the geometric principles applied.

The missing angles are:
1) 30°
2) 75°
3) 37°
4) 72° and 72°
5) 190°
6) 60°