Word Problems on Lines and Angles
Word problems on lines and angles require you to use angle relationships — complementary, supplementary, vertically opposite, and parallel line properties — to set up equations and find unknown angles.
The key is to identify which angle relationship applies and write the correct equation.
What is Word Problems on Lines and Angles - Grade 7 Maths (Lines and Angles)?
Angle relationships used:
- Complementary angles: Sum = 90°
- Supplementary angles: Sum = 180°
- Linear pair: Sum = 180°
- Vertically opposite: Equal
- Angles on parallel lines: Corresponding (equal), alternate interior (equal), co-interior (sum = 180°)
Word Problems on Lines and Angles Formula
Setting up equations:
- Identify the relationship between the angles.
- Write the equation (e.g., x + 2x = 90°).
- Solve for x.
- Find each angle.
Types and Properties
Common problem types:
- Find the complement of a given angle.
- Two supplementary angles are in a given ratio — find them.
- Find angles formed by parallel lines and a transversal.
- Find unknown angles in a triangle using angle sum property.
Solved Examples
Example 1: Complementary Angles
Problem: Two complementary angles are in the ratio 2:3. Find the angles.
Solution:
- Let angles = 2x and 3x.
- 2x + 3x = 90° → 5x = 90° → x = 18°
- Angles: 2 × 18 = 36° and 3 × 18 = 54°
Answer: 36° and 54°.
Example 2: Supplementary Angles
Problem: One angle is 40° more than its supplement. Find both angles.
Solution:
- Let one angle = x, other = x + 40°.
- x + x + 40 = 180 → 2x = 140 → x = 70°
- Other angle = 110°
Answer: 70° and 110°.
Example 3: Linear Pair
Problem: Two angles form a linear pair. One is 3 times the other. Find them.
Solution:
- Let angles = x and 3x.
- x + 3x = 180° → 4x = 180° → x = 45°
- Angles: 45° and 135°
Answer: 45° and 135°.
Example 4: Parallel Lines
Problem: Two parallel lines are cut by a transversal. One angle is 65°. Find its co-interior angle.
Solution:
- Co-interior angles sum = 180°.
- Other angle = 180° − 65° = 115°
Answer: 115°.
Real-World Applications
Real-world uses:
- Architecture: Calculating roof angles, door/window angles.
- Navigation: Bearings and directions use angle calculations.
- Sports: Angles of release in javelin/shot put affect distance.
Key Points to Remember
- Complementary: sum = 90°.
- Supplementary: sum = 180°.
- Linear pair: sum = 180°.
- Vertically opposite angles are equal.
- Set up equations using the relationship, then solve for the unknown.
Practice Problems
- Two supplementary angles are in ratio 5:4. Find them.
- Find the complement of 37°.
- Two angles form a linear pair. One is 2x + 10° and the other is 3x. Find x.
- A transversal cuts two parallel lines. One alternate interior angle is 72°. Find the other.
Frequently Asked Questions
Q1. How do you find complementary angles?
Two angles are complementary if their sum is 90°. If one angle is x, its complement is 90° − x.
Q2. How do you find supplementary angles?
Two angles are supplementary if their sum is 180°. If one angle is x, its supplement is 180° − x.
Q3. What are co-interior angles?
Co-interior angles (same-side interior angles) are formed between parallel lines on the same side of a transversal. Their sum is 180°.
