Does the 180° rule apply to all triangles?

Yes — acute, right, or obtuse. It is universal in Euclidean geometry.

What is the exterior angle theorem?

An exterior angle equals the sum of the two non-adjacent interior angles. Follows directly from the 180° rule.

What common mistakes should I watch for?

Subtracting from 360° instead of 180°, or forgetting to add both known angles before subtracting.

Triangle Angle Sum Worksheet

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Triangle Angle Sum Worksheet

Name:Date:Class:

1.A triangle has angles

66°

and

15°

. Find the third angle.

2.A triangle has angles

32°

and

51°

. Find the third angle.

3.A triangle has angles

38°

and

100°

. Find the third angle.

4.A triangle has angles

24°

and

102°

. Find the third angle.

5.A triangle has angles

92°

and

47°

. Find the third angle.

6.A triangle has angles

68°

and

20°

. Find the third angle.

7.A triangle has angles

57°

and

16°

. Find the third angle.

8.A triangle has angles

36°

and

25°

. Find the third angle.

9.A triangle has angles

114°

and

51°

. Find the third angle.

10.A triangle has angles

65°

and

66°

. Find the third angle.

11.A triangle has angles

20°

and

90°

. Find the third angle.

12.A triangle has angles

25°

and

79°

. Find the third angle.

13.A triangle has angles

75°

and

25°

. Find the third angle.

14.A triangle has angles

55°

and

78°

. Find the third angle.

15.A triangle has angles

128°

and

37°

. Find the third angle.

16.A triangle has angles

67°

and

37°

. Find the third angle.

17.A triangle has angles

37°

and

122°

. Find the third angle.

18.A triangle has angles

100°

and

42°

. Find the third angle.

19.A triangle has angles

52°

and

47°

. Find the third angle.

20.A triangle has angles

19°

and

58°

. Find the third angle.

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Worked Example

Problem: In triangle PQR, P = 65°, Q = 48°. Find R.

65° + 48° + R = 180°— Triangle angle sum.
113° + R = 180°— Add known angles.
R = 67°— Subtract from 180°.

Answer: 67°

Triangle Angle Sum Worksheet

Triangle Angle Sum Worksheet

Answer Key

Worked Example

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