Let’s solve each problem one by one.
---
Top Left (Must Know):
We have a triangle with two interior angles: 50° and 70°. The third angle is not labeled, but we’re asked for the exterior angle x at the bottom right corner.
Remember: An exterior angle of a triangle equals the sum of the two opposite interior angles.
So, x = 50° + 70° =
120°
✔ Check: The third interior angle would be 180° - 50° - 70° = 60°. Then x + 60° = 180° → x = 120°. Correct.
---
Top Right (Must Know):
Triangle has angles 65° and 45°. We need to find exterior angle x at the bottom left.
Again, exterior angle = sum of the two opposite interior angles.
Opposite interior angles to x are 65° and 45°.
So, x = 65° + 45° =
110°
✔ Check: Third interior angle = 180° - 65° - 45° = 70°. Then x + 70° = 180° → x = 110°. Correct.
---
Bottom Left (Good to Know):
Triangle ABC, with angles at C = 62°, A = 51°. So angle at B (inside triangle) = 180° - 62° - 51° =
67°
Now, y° is the interior angle at B → so
y = 67
x° is the exterior angle at B (on line D-B-A). Exterior angle = sum of opposite interior angles = 62° + 51° =
113°
Also, x + y = 180° → 113 + 67 = 180. Correct.
So:
x = 113
y = 67
---
Bottom Right (Good to Know):
Triangle ABC, angle at C = 70°. Angles at A and B (interior) are both labeled x° → so it’s an isosceles triangle.
Sum of angles in triangle = 180°
So: x + x + 70 = 180
→ 2x = 110
→ x = 55
Then y° is the exterior angle at B → y = sum of opposite interior angles = x + 70 = 55 + 70 =
125
Check: y + x = 125 + 55 = 180 → correct.
So:
x = 55
y = 125
---
Final Answers:
Top Left: x = 120
Top Right: x = 110
Bottom Left: x = 113, y = 67
Bottom Right: x = 55, y = 125
Final Answer:
x = 120°, x = 110°, x = 113°, y = 67°, x = 55°, y = 125°
Parent Tip: Review the logic above to help your child master the concept of interior and exterior angles worksheet.
