In the given figure, ABC is a triangle. The bisectors of internal ∠B and external ∠C interest at D. If ∠BDC = 48°, then what is the value (in degrees) of ∠A? <img src="https://cracku.in/media/uploads/blob

1. In the given figure, ABC is a triangle. The bisectors of internal ∠B and external ∠C interest at D. If ∠BDC = 48°, then what is the value (in degrees) of ∠A?

Write Comment

Comments

By: anil on 05 May 2019 01.48 am

Let $$angle$$ A = $$ heta$$
Using exterior angle property, => $$ heta+2y=2x$$ => $$2(x-y)= heta$$ => $$x-y=frac{ heta}{2}$$ ------------(i) In $$ riangle$$ ABC, => ∠A + ∠B + ∠C = 180 => $$ heta+2y+angle ACB=180^circ$$ => $$angle ACB = 180^circ-2y- heta$$ Thus, ∠DCB = ∠ACB + ∠ACD = $$180^circ-2y- heta+x$$ -----------(ii) Now, in $$ riangle$$ BCD, => ∠DBC + ∠DCB + ∠CDB = 180 => $$y+(180^circ-2y- heta+x)+48^circ=180^circ$$ => $$x-y- heta=-48^circ$$ Substituting value from equation (i), we get : => $$frac{ heta}{2}- heta=-48^circ$$ => $$frac{ heta}{2}=48^circ$$ => $$ heta=48 imes2=96^circ$$ => Ans - (B)

Tags

Show Similar Question And Answers

QA->The difference between compound interest and simple interest for an amount in 2 years is Rs.If the rate of interest is 8%, the amount is :....

QA->A well conditioned triangle should not have angles more than ..........degrees.....

QA->In a triangle when two adjacent sides a & b and their included angle "C" are given in then its area will be:....

QA->Currency whose face value is higher than the internal value is called?....

QA->Work done by all the forces(external and internal) on a system equals the change in :....

MCQ->In the given figure, ABC is a triangle. The bisectors of internal ∠B and external ∠C interest at D. If ∠BDC = 48°, then what is the value (in degrees) of ∠A?

....

MCQ-> A game of strategy, as currently conceived in game theory, is a situation in which two or more “players” make choices among available alternatives (moves). The totality of choices determines the outcomes of the game, and it is assumed that the rank order of preferences for the outcomes is different for different players. Thus the “interests” of the players are generally in conflict. Whether these interests are diametrically opposed or only partially opposed depends on the type of game.Psychologically, most interesting situations arise when the interests of the players are partly coincident and partly opposed, because then one can postulate not only a conflict among the players but also inner conflicts within the players. Each is torn between a tendency to cooperate, so as to promote the common interests, and a tendency to compete, so as to enhance his own individual interests.Internal conflicts are always psychologically interesting. What we vaguely call “interesting” psychology is in very great measure the psychology of inner conflict. Inner conflict is also held to be an important component of serious literature as distinguished from less serious genres. The classical tragedy, as well as the serious novel, reveals the inner conflict of central figures. The superficial adventure story, on the other hand, depicts only external conflict; that is, the threats to the person with whom the reader (or viewer) identifies stem in these stories exclusively from external obstacles and from the adversaries who create them. On the most primitive level this sort of external conflict is psychologically empty. In the fisticuffs between the protagonists of good and evil, no psychological problems are involved or, at any rate, none are depicted in juvenile representations of conflict.The detective story, the “adult” analogue of a juvenile adventure tale, has at times been described as a glorification of intellectualized conflict. However, a great deal of the interest in the plots of these stories is sustained by withholding the unraveling of a solution to a problem. The effort of solving the problem is in itself not a conflict if the adversary (the unknown criminal) remains passive, like Nature, whose secrets the scientist supposedly unravels by deduction. If the adversary actively puts obstacles in the detective’s path toward the solution, there is genuine conflict. But the conflict is psychologically interesting only to the extent that it contains irrational components such as a tactical error on the criminal’s part or the detective’s insight into some psychological quirk of the criminal or something of this sort. Conflict conducted in a perfectly rational manner is psychologically no more interesting than a standard Western. For example, Tic-tac-toe, played perfectly by both players, is completely devoid of psychological interest. Chess may be psychologically interesting but only to the extent that it is played not quite rationally. Played completely rationally, chess would not be different from Tic-tac-toe.In short, a pure conflict of interest (what is called a zero-sum game) although it offers a wealth of interesting conceptual problems, is not interesting psychologically, except to the extent that its conduct departs from rational norms.According to the passage, internal conflicts are psychologically more interesting than external conflicts because
....

MCQ->ABC is a triangle. The bisectors of the internal angle $$\angle$$B and external $$\angle$$C intersect at D. If $$\angle$$BDC=$$50^{\circ}$$, then $$\angle$$A is....

MCQ-> The CEO of ABC Telecom Ltd. (ABC) is in a quandary since he received the telephone call in the morning from his counterpart at LMN Telecom Ltd. (LMN). Both companies were engaged in a bitter experience a couple of years ago when they had attempted to merge with the intention of creating a behemoth telecom company, possibly the largest in the world. The merger had fallen through due to opportunistic behavior on the part of Mr. Das, then CEO of LMN. During the time the merger talks were taking place, Mr. Das had also approached a few other suitors for LMN in an attempt to force ABC to pay a higher price. Further, there were reports of attempts by management of LMN to scuttle the deal. Back then, ABC had also faced stiff opposition to the deal from one of its large shareholders. Since then, a lot has changed for both companies. The bleak economic conditions due to recession had led to a drastic fall in the market value of both companies, with ABC comparatively losing much more in terms of market value. Raising money has become more difficult for both companies, especially for LMN. On the brighter side for ABC, the opposing shareholder had recently sold off his stake to another investor who earlier had supported the original merger deal with LMN a couple of years ago.Which of the following would be the most appropriate line (s) of thought for the CEO of ABC to adopt in response to the offer by LMN? I. Once bitten twice shy. There is simply no way I can think of resuming talks with LMN after their unethical behaviour the previous time around. I would rather spend my time on merger discussions with other companies. Ii. The deal may make less business sense this time around. However, if it goes through, I will become the CEO of the world’s largest telecom company. So let us try our luck once more. Iii. I will resume talks only if they provide guarantees as to the reimbursement of our expenses incurred, in the event of the deal not materializing. Iv. Let me not be biased against dealing with LMN, if we can secure the deal at a reasonably low price, benefiting our shareholders, let us go ahead with it. V. I am not sure if we can raise the money now. In any event, they are the ones facing greater financial problems. So let’s not hurry now. We might have an opportunity to buy them out at a cheaper price later.....

MCQ-> The English alphabet is divided into five groups. Each group starts with the vowel and the consonants immediately following that vowel and the consonants immediately following that vowel are included in that group. Thus, the letters A, B, C, D will be in the first group, the letters E, F, G, H will be in the second group and so on. The value of the first group is fixed as 10, the second group as 20 and so on. The value of the last group is fixed as 50. In a group, the value of each letter will be the value of that group. To calculate the value of a word, you should give the same value of each of the letters as the value of the group to which a particular letter belongs and then add all the letters of the word: If all the letters in the word belong to one group only, then the value of that word will be equal to the product of the number of letters in the word and the value of the group to which the letters belong. However, if the letters of the words belong to different groups, then first write the value of all the letters. The value of the word would be equal to the sum of the value of the first letter and double the sum of the values of the remaining letters.For Example : The value of word ‘CAB’ will be equal to 10 + 10 + 10 = 30, because all the three letters (the first letter and the remaining two) belong to the first group and so the value of each letter is 10. The value of letter BUT = $$10 + 2 \times 40 + 2 \times 50 = 190$$ because the value of first letter B is 10, the value of T = 2 $$\times$$ 40 (T belongs to the fourth group) and the value of U = 2 $$\times$$ 50 (U belongs to the fifth group). Now calculate the value of each word given in questions 161 to 165 :AGE
....