Angle sum and exterior angle of a triangle: Class 7 practice
The three interior angles of any triangle add to 180°. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Types of angles
- Linear pair (180°)
The idea behind angle sum and exterior angle of a triangle
The three interior angles of any triangle add to 180°. An exterior angle equals the sum of the two interior opposite angles.
Step-by-step method
- Add the known angles.
- Subtract from 180°.
- For ratios, let the angles be kx and solve kx-sum = 180.
Worked example 1 (Basic)
Two angles of a triangle are 79° and 56°. Find the third.
- 180° − (79° + 56°) = 45°
- Answer: 45°
Worked example 2 (Standard)
The angles of a triangle are in the ratio 2 : 6 : 4. Find them.
- 2x + 6x + 4x = 180°
- x = 15°
- Answer: 30°, 90°, 60°
Worked example 3 (Challenge)
An exterior angle of a triangle is 96° and one interior opposite angle is 50°. Find the other interior opposite angle and the adjacent interior angle.
- Other opposite angle = 96 − 50 = 46°
- Adjacent interior = 180 − 96 = 84°
- Answer: 46° and 84°
Common mistakes and misconceptions
- Using 360° (that is for quadrilaterals)
- Adding the adjacent interior angle in exterior-angle questions
Practice questions
- (Basic) Two angles of a triangle are 46° and 80°. Find the third.
- (Basic) Two angles of a triangle are 74° and 40°. Find the third.
- (Standard) The angles of a triangle are in the ratio 3 : 1 : 5. Find them.
- (Standard) The angles of a triangle are in the ratio 1 : 2 : 6. Find them.
- (Challenge) An exterior angle of a triangle is 140° and one interior opposite angle is 30°. Find the other interior opposite angle and the adjacent interior angle.
- (Challenge) An exterior angle of a triangle is 118° and one interior opposite angle is 64°. Find the other interior opposite angle and the adjacent interior angle.
Answer key with full working
- Q1: 180° − (46° + 80°) = 54° → Answer: 54°
- Q2: 180° − (74° + 40°) = 66° → Answer: 66°
- Q3: 3x + 1x + 5x = 180° → x = 20° → Answer: 60°, 20°, 100°
- Q4: 1x + 2x + 6x = 180° → x = 20° → Answer: 20°, 40°, 120°
- Q5: Other opposite angle = 140 − 30 = 110° → Adjacent interior = 180 − 140 = 40° → Answer: 110° and 40°
- Q6: Other opposite angle = 118 − 64 = 54° → Adjacent interior = 180 − 118 = 62° → Answer: 54° and 62°
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 angle sum and exterior angle of a triangle 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.