Filtering With Basic Angle Facts - Opinions Nobody Asked For - Free Printable

I'll solve each diagram step by step to find the angle marked x.

Diagram 1 (top left):
- Left triangle has angles: 90°, 65°, and one unknown = 180° - 90° - 65° = 25°
- Right triangle has angles: 90°, 35°, and one unknown = 180° - 90° - 35° = 55°
- The angle x is formed where the two triangles intersect
- Looking at the small triangle in the middle with angles: 25°, 55°, and x
- x = 180° - 25° - 55° = 100°

Diagram 2 (top middle):
- Left triangle has angles: 90°, 30°, and one unknown = 180° - 90° - 30° = 60°
- Right triangle has angles: 90°, 70°, and one unknown = 180° - 90° - 70° = 20°
- The angle x is in a triangle with angles: 60°, 20°, and x
- x = 180° - 60° - 20° = 100°

Diagram 3 (top right):
- Left triangle has angles: 90°, 60°, and one unknown = 180° - 90° - 60° = 30°
- Right triangle has angles: 90°, 45°, and one unknown = 180° - 90° - 45° = 45°
- The angle x is in a triangle with angles: 30°, 45°, and x
- x = 180° - 30° - 45° = 105°

Diagram 4 (bottom left):
- The tick marks show these are isosceles triangles
- Right triangle has angles: 90°, 70°, and one unknown = 180° - 90° - 70° = 20°
- Since it's isosceles, the other base angle is also 20°
- The angle x is supplementary to 20° (they form a straight line)
- x = 180° - 20° = 160°

Wait, let me reconsider diagram 4 more carefully:
- Right triangle: 90°, 70°, and third angle = 20°
- The angle adjacent to x on the bottom is 20°
- x and 20° form a linear pair
- x = 180° - 20° = 160°

Actually, looking more carefully at diagram 4, x appears to be an interior angle of a triangle. Let me recalculate:
- The triangle containing x has one angle of 20° (from the right triangle)
- Due to the isosceles property shown by tick marks, we need to identify which sides are equal
- If the two legs with tick marks are equal, then those opposite angles are equal
- The angle at the bottom right is 20°, so if this is an isosceles triangle, another angle is also 20°
- Then x = 180° - 20° - 20° = 140°

Let me look at this more systematically. In diagram 4, I see tick marks on two sides of the left triangle, making it isosceles. The right triangle has angles 90°, 70°, 20°. The angle x appears to be vertically opposite or part of a triangle. Given the configuration, x = 180° - 20° = 160° seems most likely.

Diagram 5 (bottom middle):
- We have a 100° angle shown
- Right triangle has angles: 90°, 45°, and one unknown = 180° - 90° - 45° = 45°
- The 100° angle and the angle next to it form a linear pair, so that angle = 180° - 100° = 80°
- The triangle containing x has angles: 80°, 45°, and x
- x = 180° - 80° - 45° = 55°

Diagram 6 (bottom right):
- We have a 110° angle shown
- The tick marks indicate an isosceles triangle
- The angle adjacent to 110° forms a linear pair: 180° - 110° = 70°
- Since it's isosceles (shown by tick marks), another angle is also 70°
- The third angle of that triangle = 180° - 70° - 70° = 40°
- Angle x and 40° are vertically opposite, so x = 40°

Let me verify my calculations once more:

Diagram 1: ✓ x = 100°
Diagram 2: ✓ x = 100°
Diagram 3: ✓ x = 105°
Diagram 4: Need to reconsider...
Diagram 5: ✓ x = 55°
Diagram 6: ✓ x = 40°

For Diagram 4, looking at the structure again: there's a right triangle on the right with 70°, giving us 20°. The left triangle has tick marks showing it's isosceles. The angle x appears to be where lines cross. If we consider the triangle containing x, and knowing one angle is 20°, and using properties of isosceles triangles and vertical angles, x = 160°.

Final Answer:
Diagram 1: x = 100°
Diagram 2: x = 100°
Diagram 3: x = 105°
Diagram 4: x = 160°
Diagram 5: x = 55°
Diagram 6: x = 40°