To find the unknown angles, I will use the rule that the sum of all interior angles in a triangle is always 180°.
Problem 1:
The known angles are 18° and 145°.
Sum of known angles = 18 + 145 = 163°
Unknown angle x = 180 - 163 = 17°
Problem 2:
The known angles are 85° and 55°.
Sum of known angles = 85 + 55 = 140°
Unknown angle x = 180 - 140 = 40°
Problem 3:
The known angles are 70° and 70°.
Sum of known angles = 70 + 70 = 140°
Unknown angle x = 180 - 140 = 40°
Problem 4:
The known angles are 55° and 75°.
Sum of known angles = 55 + 75 = 130°
Unknown angle x = 180 - 130 = 50°
Problem 5:
This figure shows a square divided by a diagonal into two triangles. Looking at the top-left triangle formed by the diagonal:
- The top-left corner of the square is a right angle (90°). It is split into a 45° angle and the unknown angle x°. So, x = 90 - 45 = 45°.
- Alternatively, looking at the bottom-right triangle: The bottom-right corner is also 90°, split into 45° and x°. So, x = 90 - 45 = 45°.
- We can verify using the triangle sum rule for the top-left triangle: The angles are x°, 45°, and the angle at the other end of the diagonal. Since it's a square cut diagonally, the triangle is an isosceles right triangle with angles 45°, 45°, and 90°. Thus x = 45°.
Final Answer:
1. X = 17°
2. X = 40°
3. X = 40°
4. X = 50°
5. X = 45°
Parent Tip: Review the logic above to help your child master the concept of triangle interior angles worksheet.
