Lines And Angles
NIOS · Class 10 · Maths
Flashcards for Lines And Angles — NIOS Class 10 Maths. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedSolve: If a ray stands on a line, the two adjacent angles are 68° and x°. Find x.
Answer
Step 1: Use the linear pair rule. Step 2: Their sum is 180°. Step 3: 68° + x = 180°. Step 4: x = 180° - 68° = 112°. Answer: x = 112°.
Solve: Two angles are supplementary. One angle is 105°. Find the other angle.
Answer
Step 1: Supplementary angles add up to 180°. Step 2: Let the other angle be x. Step 3: 105° + x = 180°. Step 4: x = 180° - 105° = 75°. Answer: 75°.
Solve: Two angles are complementary. One angle is 37°. Find the other angle.
Answer
Step 1: Complementary angles add up to 90°. Step 2: Let the other angle be x. Step 3: 37° + x = 90°. Step 4: x = 90° - 37° = 53°. Answer: 53°.
Why are vertically opposite angles equal when two lines intersect?
Answer
When two lines intersect, each pair of adjacent angles forms a linear pair. Linear pairs sum to 180°. So each angle in one pair equals the angle opposite to it, because both are supplementary to the s…
Solve: Two intersecting lines form one angle of 125°. Find the vertically opposite angle and one adjacent angle.
Answer
Step 1: Vertically opposite angles are equal, so the opposite angle = 125°. Step 2: Adjacent angles form a linear pair. Step 3: Adjacent angle = 180° - 125° = 55°. Answer: opposite angle = 125°, adjac…
Solve: If one angle of a linear pair is (5x + 10)° and the other is x°, find x.
Answer
Step 1: A linear pair sums to 180°. Step 2: Write the equation: x + (5x + 10) = 180. Step 3: 6x + 10 = 180. Step 4: 6x = 170. Step 5: x = 170/6 = 28 1/3°. Answer: x = 28 1/3°.
When do you use the formula for corresponding angles being equal?
Answer
Use it when a transversal cuts two parallel lines. Then the matching angles are equal: ∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8. Example: if ∠1 = 80°, then ∠5 = 80°.
Solve: Two parallel lines are cut by a transversal. If one corresponding angle is 48°, find the angle corresponding to it and its adjacent supplementary angle.
Answer
Step 1: Corresponding angles on parallel lines are equal. Step 2: So the corresponding angle = 48°. Step 3: The adjacent angle on a straight line is supplementary. Step 4: Adjacent angle = 180° - 48° …
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