In ΔABC, ∠C = 54°, the perpendicular bisector of AB at D meets BC at E. If ∠EAC = 42°, then what is the value (in degrees) of ∠ABC? ?->(Show Answer!)

1. In ΔABC, ∠C = 54°, the perpendicular bisector of AB at D meets BC at E. If ∠EAC = 42°, then what is the value (in degrees) of ∠ABC?

Write Comment

Comments

By: anil on 05 May 2019 02.26 am

Given : ED is the perpendicular bisectors of AB, $$angle C=54^circ$$ and $$angle EAC=y=42^circ$$
To find : $$angle B=x=?$$ Solution : In $$ riangle$$ EAC, using exterior angle property, => $$angle$$ AEB = $$angle$$ C + $$y$$ => $$angle$$ AEB = $$54^circ+42^circ=96^circ$$ Thus, in $$ riangle$$ AEB, => $$x+z=180^circ-96^circ=84^circ$$ ------------(i) Also, in $$ riangle$$ EAD and $$ riangle$$ BDE AD = DB (DE bisects AB) $$angle$$ EAD = $$angle$$ EDB = $$90^circ$$ DE = DE (Common) Thus, $$ riangle$$ EAD $$cong$$ $$ riangle$$ BDE (By SAS criterion) => $$x=z$$ (By CPCT) Substituting above value in equation (i), we get : => $$x+x=2x=84^circ$$ => $$x=frac{84}{2}=42^circ$$ => Ans - (B)

Tags

Show Similar Question And Answers

QA->The type of gears used for transmitting power between two-non intersecting perpendicular shafts is :....

QA->Economic development that meets the needs of the present without compromising the ability of future generations to meet their own needs is ?....

QA->Economic development that meets the needs of the present without compromising the ability of future generations to meet their own needs is :....

QA->A cyclist goes 40 km towards East and then turning to right he goes 40 km. Again he turn to his left and goes 20 km. After this he turns to his left and goes 40 km, then again turns right and goes 10km. How far is he from his starting point?....

QA->Jose travels 7 km to the north.Then again he turns to the right and walks 3 km.Then again he turns to his right and moves 7 km forward.How many kilometers away is he from the starting point?....

MCQ->In ΔABC, ∠C = 54°, the perpendicular bisector of AB at D meets BC at E. If ∠EAC = 42°, then what is the value (in degrees) of ∠ABC?....

MCQ->In triangle ABC, AB = 12 cm, ∠B = 60°, the perpendicular from A to BC meets it at D. The bisector of ∠ABC meets AD at E. Then E divides AD in the ratio....

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
....

MCQ-> Analyse the following caselet and answer the question that follow: Nicky, Manoj and Benita are graduates from a top ranked B-school. They joined ABC corporation a year ago. ABC is known for its performance oriented culture. This is the first time the organization recruited from a top ranked B-school. They are part of a five member team with two others from lower ranked B-schools. Nicky, Manoj and Benita draw 40 percent higher salaries than other team members. This team reports to Amelia Ganeshmurthi, a senior Executive.Amelia is disappointed with the performance of Nicky, Manoj and Benita. She came to know that ABC was not their first choice and they had spent the first ten months applying to other organizations. However, they have now started liking ABC and promised to do their best henceforth. Amelia has to rate their annual performance and decide about their future. She has the following choices: 1. Fire them from ABC for insincerity and save the organization’s time and money. 2. Given them average ratings with a year to prove their worth and fire them from ABC if they fail to show significant progress. 3. Impose a pay-cut of 15% since they have not delivered on the promise, but give them relatively high ratings. 4. Given them relatively poor ratings with one year time to improve and fire them from ABC if they fail to show significant progress. 5. Give them high ratings and give them a second chance to prove their worth. Which of the following options rank the above choices in the order of MOST APPROPRIATE to LEAST APPROPRIATE?....