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In the given figure, LMPN is a trapezium with LM || NP, ∠MPO = 30° and MO ⊥ NP. What is the measure of ∠LNO if ∠LMP = 2∠LNO?
  • a)
    55°
  • b)
    65°
  • c)
    75°
  • d)
    85°
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
In the given figure, LMPN is a trapezium with LM || NP, ∠MPO = 30° an...
Given: ∠MPO = 30° and MO⊥NP
In triangle MPO,
∠MOP + ∠OPM + ∠PMO = 180° (Sum of interior angles of a triangle)
90° + 30° + ∠PMO = 180°
120° + ∠PMO = 180°
∠PMO = 60°
Now, ∠LMP = 90° + 60°
∠LMP = 150°
Given: ∠LMP = 2∠LNO
2∠LNO = 150°
∠LNO = 75°
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In each of the following questions series begins with unnumbered figure on he extreme left. One and only one of the five numbered figures in the series does not fit into the series. The two unnumbered figures one each on the extreme left and the extreme right fit into the series. You have to take as many aspects into account as possible of the figures in the series and find out the one and only one of the five numbered figures which does not fit into the series. The number of that figure is the answer.Study the following question.In this question, the number of lines in the figures goes on increasing one from left to right. If we go by this aspect of number of lines’ only then there is no wrong figure in the series. But if we also consider the ‘manner’ in which the ‘number of lines’ in the figures goes on increasing from left to right we come to know that the figure No. 4 does not fit into the series. Therefore, 4 is the answer.

In each of the following questions series begins with unnumbered figure on the extreme left. One and only one of the five numbered figures in the series does not fit into the series. The two unnumbered figures one each on the extreme left and the extreme right fit into the series. You have to take as many aspects into account as possible of the figures in the series and find out the one and only one of the five numbered figures which does not fit into the series. The number of that figure is the answer.Study the following question.In this question, the number of lines in the figures goes on increasing one from left to right. If we go by this aspect of number of lines’ only then there is no wrong figure in the series. But if we also consider the ‘manner’ in which the ‘number of lines’ in the figures goes on increasing from left to right we come to know that the figure No. 4 does not fit into the series. Therefore, 4 is the answer.

In each of these questions there are two sets of figures. The figures on the left are Problem Figures(four figures and one question-marked spac e) and those on the right are Answer Figures indicated by number 1, 2, 3, 4 and 5. A series is established if one of the five Answer Figures is placed at the "question-marked space". Problem Figures form a series if they change from left to right according to some rule. The number of the Answer Figure which should be placed in the question-marked space, is the answer. All the five figures, ie four Problem Figures and one Answer Figure placed in the question-marked space should be considered as forming the series.Study the following question.If we place the Answer Figure 4 in the question marked space it makes a series which indicates that one vertical line isadded in each figure. So the answer is '4', Note that if we go by only one aspect of number of lines', Answer Figure 3 may also fit in. So you have to consider all different aspects.Now solve the following questions.

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In the given figure, LMPN is a trapezium with LM || NP, ∠MPO = 30° and MO ⊥ NP. What is the measure of ∠LNO if ∠LMP = 2∠LNO?a)55°b)65°c)75°d)85°Correct answer is option 'C'. Can you explain this answer?
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