Lines and Angles — Flashcards
Karnataka Board · Class 9 · Mathematics
20 flashcards for Lines and Angles (Karnataka Board Class 9 Mathematics) to test yourself on key terms and facts.
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Two lines AB and CD intersect at point O. If ∠AOC = 65°, find ∠BOD.
Answer
Step 1: Identify that ∠AOC and ∠BOD are vertically opposite angles. Step 2: Apply Theorem - Vertically opposite angles are equal. Step 3: Therefore, ∠BOD = ∠AOC = 65°. Answer: ∠BOD = 65°…
A ray OC stands on line AB. If ∠AOC : ∠BOC = 3:2, find both angles.
Answer
Step 1: Since ray OC stands on line AB, ∠AOC + ∠BOC = 180° (Linear Pair Axiom). Step 2: Let ∠AOC = 3x and ∠BOC = 2x. Step 3: 3x + 2x = 180° → 5x = 180° → x = 36°. Step 4: ∠AOC = 3(36°) = 108° and ∠BOC…
Lines PQ and RS intersect at O. If ∠POR : ∠ROQ = 5:7, find all four angles.
Answer
Step 1: ∠POR + ∠ROQ = 180° (Linear pair). Step 2: Let ∠POR = 5x and ∠ROQ = 7x. Step 3: 5x + 7x = 180° → 12x = 180° → x = 15°. Step 4: ∠POR = 5(15°) = 75°, ∠ROQ = 7(15°) = 105°. Step 5: ∠POS = ∠ROQ = 1…
Two parallel lines AB and CD are cut by transversal EF. If one interior angle is 110°, find its co-interior angle.
Answer
Step 1: Identify that co-interior angles are interior angles on the same side of transversal. Step 2: Apply theorem - Sum of co-interior angles = 180° when lines are parallel. Step 3: Let co-interior …
Lines AB || CD. Transversal PQ cuts them. If ∠APQ = 65°, find ∠PQD (corresponding angle).
Answer
Step 1: Identify that ∠APQ and ∠PQD are corresponding angles. Step 2: Apply theorem - Corresponding angles are equal when lines are parallel. Step 3: Therefore, ∠PQD = ∠APQ. Step 4: ∠PQD = 65°. Answer…
AB || CD, transversal EF. If alternate interior angle is 45°, find the other alternate interior angle.
Answer
Step 1: Identify the alternate interior angles. Step 2: Apply theorem - Alternate interior angles are equal when lines are parallel. Step 3: If one alternate interior angle = 45°, then the other = 45°…
Find the value of x: Two adjacent angles are (3x + 10)° and (2x + 20)°. They form a linear pair.
Answer
Step 1: Adjacent angles forming linear pair sum to 180°. Step 2: (3x + 10)° + (2x + 20)° = 180°. Step 3: 3x + 10 + 2x + 20 = 180. Step 4: 5x + 30 = 180. Step 5: 5x = 150. Step 6: x = 30. Answer: x = 3…
When do you use the Linear Pair Axiom? Give an example.
Answer
Use when: A ray stands on a line, creating two adjacent angles. Theorem: Sum of adjacent angles = 180°. Example: Ray OC on line AB creates ∠AOC and ∠BOC. ∠AOC + ∠BOC = 180°. If ∠AOC = 110°, then ∠BOC …
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
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