InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
In ΔABC, a line parallel to BC cuts a B and AC at X and Y(a) If AB = 3.6cm, AC = 2.4cm, AX = 2.1 cm, what is the length of AY?(b) If AB = 2cm, AC = 1.5cm, AY = 0.9cm what is the length of BX? |
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Answer» a. \(\frac{AB}{AX}=\frac{AC}{AY}\) \(\Rightarrow \frac{3.6}{2.1}=\frac{2.4}{AY};\) ⇒ 3.6 × AY = 2.4 × 2.1 ⇒ AY = 1.4 cm b. Let length of AX = x cm \(\frac{AX}{AB}=\frac{AY}{AC}\) \(\Rightarrow \frac{x}{2}=\frac{0.9}{1.5};\) \(1.5\times x=1.8\) ⇒ x = 1.2; BX = AB – AX; BX = 2 – 1.2 = 0.8 cm |
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| 2. |
Prove that, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also.Given: line AB || line CD and line EF intersects them at P and Q respectively.line EF ⊥ line ABTo prove: line EF ⊥ line CD |
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Answer» Proof: line EF ⊥ line AB[Given] ∴ ∠APR = 90° ….(i) line AB || line CD and line EF is their transversal. ∴ ∠EPB ≅ ∠PQD …..(ii) [Corresponding angles] ∴ ∠PQD = 90° [From (i) and (ii)] ∴ line EF ⊥ line CD |
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| 3. |
In the given figure, how will you decide whether line ¡ and line m are parallel or not? |
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Answer» In the figure, we observe that line I and line m are coplanar and do not intersect each other. ∴ Line l and line m are parallel lines. |
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| 4. |
In the given figure, line RP || line MS and line DK is their transversal. ∠DHP = 85°. Find the measures of following angles.i. ∠RHD ii. ∠PHG iii. ∠HGS iv. ∠MGK |
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Answer» i. ∠DHP = 85° …..(i) ∠DHP + ∠RHD = 180° [Angles in a linear pair] 85° + ∠RHD = 180° ∴ ∠RHD = 180°- 85° ∴ ∠RHD = 95° …..(ii) ii. ∠PHG = ∠RHD [Vertically opposite angles] ∴ ∠PHG = 95° [From (ii)] iii. line RP || line MS and line DK is their transversal. [Corresponding angles] ∴ ∠HGS = ∠DHP …..(iii) [From (i)] iv. ∠HGS = 85° [Vertically opposite angles] ∴ ∠MGK = ∠HGS ∠MGK = 85° [From (iii)] |
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| 5. |
The number of angles formed by a transversal of two lines is _____. (A) 2 (B) 4 (C) 8 (D) 16 |
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Answer» (C) The answer is 8 |
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| 6. |
Select the correct alternative and fill in the blanks in the following statement.If a transversal intersects two parallel lines then the sum of interior angles on the same side of the transversal is ____. (A) 0° (B) 90° (C) 180° (D) 360° |
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Answer» (C) The answer is 180° |
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| 7. |
In the given figure, y = 108° and x = 71°. Are the lines m and n parallel? Justify? |
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Answer» y = 108°, x = 71° …[Given] x + y = 71° + 108° = 179° ∴ x + y = 180° ∴ The angles x andy are not supplementary. ∴ The angles do not satisfy the interior angles test for parallel lines ∴ line m and line n are not parallel lines. |
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| 8. |
In the given figure, if line AB || line CF and line BC || line ED then prove that ∠ABC = ∠FDE. |
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Answer» Given: line AB || line CF and line BC || line ED To prove: ∠ABC = ∠FDE Proof: line AB || line PF and line BC is their transversal. ∴ ∠ABC = ∠BCD ….(i) [Alternate angles] line BC || line ED and line CD is their transversal. ∴ ∠BCD = ∠FDE ….(ii) [Corresponding angles] ∴ ∠ABC = ∠FDE [From (i) and (ii)]. |
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| 9. |
In the given figure, Line AB || line CD || line EF and line QP is their transversal. If y : z = 3 : 7 then find the measure of ∠x. |
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Answer» y : z = 3 : 7 [Given] Let the common multiple be m ∴ ∠j = 3m and ∠z = 7m ….(i) line AB || line EF and line PQ is their transversal [Given] ∠x = ∠z ∴ ∠x = 7m …..(ii) [From (i)] line AB || line CD and line PQ is their transversal [Given] ∠x + ∠y = 180° ∴ 7m + 3m = 180° ∴ 10m = 180° ∴ m = 18 ∴ ∠x = 7m = 7(18°) [From (ii)] ∴ ∠x = 126° |
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| 10. |
If a transversal intersects two parallel lines then the sum of interior angles on the same side of the transversal is ____. (A) 0° (B) 90° (C) 180° (D) 360° |
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Answer» Correct option is (C) 180° |
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| 11. |
In the given figure, line AB || line CD and line PQ is transversal.Measure of one of the angles is given.Hence find the measures of the following angles.i. ∠ART ii. ∠CTQ iii. ∠DTQiv. ∠PRB |
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Answer» i. ∠BRT = 105° ….(i) ∠ART + ∠BRT = 180° [Angles in a linear pair] ∴ ∠ART + 105° = 180° ∴ ∠ART = 180° – 105° ∴ ∠ART = 75° …(ii) ii. line AB || line CD and line PQ is their transversal. ∴ ∠CTQ = ∠ART [Corresponding angles] ∴ ∠CTQ = 75° [From (ii)] iii. line AB || line CD and line PQ is their transversal. ∴ ∠DTQ = ∠BRT [Corresponding angles] ∴ ∠DTQ = 105° [From (i)] iv. ∠PRB = ∠ART [Vertically opposite angles] ∴ ∠PRB = 75° [From (ii)] |
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| 12. |
A transversal intersects two parallel lines. If the measure of one of the angles is 40°, then the measure of its corresponding angle is ______. (A) 40°(B) 140°(C) 50° (D) 180° |
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Answer» Correct option is (A) 40° |
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| 13. |
Two parallel lines are intersected by a transversal. If measure of one of the alternate interior angles is 75° then the measure of the other angle is _____. (A) 105° (B) 15°(C) 75° (D) 45° |
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Answer» Correct option is (C) 75° |
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| 14. |
In ∆ABC, ∠A = 76°, ∠B = 48°, then ∠C = _____. (A) 66° (B) 56° (C) 124°(D) 28° |
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Answer» (B) 56° In ∆ABC, ∠A + ∠B + ∠C = 180° ∴ ∠C = 180° – 76° – 48° = 56° |
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| 15. |
In ∆ABC, ∠A = 76°, ∠B = 48°, then ∠C = _____.(A) 66° (B) 56°(C) 124°(D) 28° |
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Answer» Correct option is (B) 56° In ∆ABC, ∠A + ∠B + ∠C = 180° ∴ ∠C = 180° – 76° – 48° = 56° |
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