Exterior angle property: Class 7 practice
An exterior angle of a triangle equals the sum of the two interior opposite angles. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Angle sum property
- Linear pairs
The idea behind exterior angle property
An exterior angle of a triangle equals the sum of the two interior opposite angles. It is also 180° minus the adjacent interior angle.
Step-by-step method
- Identify the exterior angle and its two opposite interior angles.
- Exterior = sum of the two opposite angles.
- Use 180° for the adjacent angle if needed.
Worked example 1 (Basic)
Two interior opposite angles of a triangle are 50° and 42°. Find the exterior angle.
- Exterior = 50° + 42° = 92°
- Answer: 92°
Worked example 2 (Standard)
An exterior angle is 105° and one interior opposite angle is 35°. Find the other interior opposite angle and the adjacent interior angle.
- Other = 105° − 35° = 70°
- Adjacent = 180° − 105° = 75°
- Answer: 70° and 75°
Worked example 3 (Challenge)
The two interior opposite angles are x and 2x, and the exterior angle is 63°. Find x.
- x + 2x = 63
- 3x = 63
- x = 21°
- Answer: 21°
Common mistakes and misconceptions
- Adding the adjacent interior angle
- Forgetting the linear pair
Practice questions
- (Basic) Two interior opposite angles of a triangle are 36° and 30°. Find the exterior angle.
- (Basic) Two interior opposite angles of a triangle are 30° and 54°. Find the exterior angle.
- (Standard) An exterior angle is 106° and one interior opposite angle is 74°. Find the other interior opposite angle and the adjacent interior angle.
- (Standard) An exterior angle is 94° and one interior opposite angle is 41°. Find the other interior opposite angle and the adjacent interior angle.
- (Challenge) The two interior opposite angles are x and 3x, and the exterior angle is 100°. Find x.
- (Challenge) The two interior opposite angles are x and 2x, and the exterior angle is 90°. Find x.
Answer key with full working
- Q1: Exterior = 36° + 30° = 66° → Answer: 66°
- Q2: Exterior = 30° + 54° = 84° → Answer: 84°
- Q3: Other = 106° − 74° = 32° → Adjacent = 180° − 106° = 74° → Answer: 32° and 74°
- Q4: Other = 94° − 41° = 53° → Adjacent = 180° − 94° = 86° → Answer: 53° and 86°
- Q5: x + 3x = 100 → 4x = 100 → x = 25° → Answer: 25°
- Q6: x + 2x = 90 → 3x = 90 → x = 30° → Answer: 30°
Syllabus note
This skill is listed under "The Triangle and its Properties" for Class 7 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is exterior angle property in?
"The Triangle and its Properties", Class 7 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.