3

enter image description here

What I did:

1)

$\angle DAB = 180-(50+75+x)$ $= 180-(125+x)$ $= 55-x$

But, that resulted in:

$50+75+55-x+x=180 \implies 180=180$ (x value not found)

2)

$\angle CPB = 180-(75+x) = 105-x$

$105-x+75+x=180 \implies 180=180$ (x value not found)

This question came in the competition that I gave today and I am in 9th class and was not able to solve this question.

The options there were:

(A) $60^\circ$

(B) $50^\circ$

(C) $55^\circ$

(D) $70^\circ$

(E) None of these

Now, please let me know how to solve this problem. PLEASE DO EXPLAIN! I want to know whether I scored full $\frac{40}{40}$ or ${39}{40}$.

I answered '(B) $50^\circ$' as I thought that the answer has to be lower than at least $55^\circ$ and $50^\circ$ was the only option of this.

Harish Chandra Rajpoot
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Rachit Bhargava
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1 Answers1

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I think that it should be clear that the only possible correct answers are (B), (C) and (E) since $\angle DCB=55^{\circ}$. If the question said "which of the following MUST be true" then the answer should be (E), because the angle denoted by $x$ can really be anything between $0^{\circ}$ and $55^{\circ}$.

DKal
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  • I want the exact answer! – Rachit Bhargava Dec 03 '13 at 11:45
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    @user2951469 I gave you the exact answer! $x$ can have any value between $0^{\circ}$ and $55^{\circ}$ and everything will be consistent. – DKal Dec 03 '13 at 11:49
  • Indeed, the answer should be (B) or (E), it cannot be 55 as $A\neq D$ –  Dec 03 '13 at 11:54
  • @John why should you assume $A\neq D$? – DKal Dec 03 '13 at 11:55
  • @DKal: Just from the picture... –  Dec 03 '13 at 11:59
  • @John I have always considered pictures in these situations as schematic, that is, instead of writing the details in a list, they are given in the form of a picture, and if you were given all these details just as a list of facts, you cannot assume $A\neq D$ unless it is explicitly stated. – DKal Dec 03 '13 at 12:04
  • @DKal You needn't assume that, they are equal! Both $D$ and $A$ subtend the same arc so they have the same angle measure. – mathematics2x2life Dec 03 '13 at 13:08
  • @mathematics2x2life, I think that you misunderstood the notation. $A$ and $D$ are points on the circle, they are not the angels $\angle CAB$ and $\angle CDB$. – DKal Dec 03 '13 at 13:15
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    @DKal Ah, then if we are referring to them as points, then I would agree with you. Diagrams may not be meant to be exact, but they certainly do not go so far as to mislead you by plotting non-distinct points! – mathematics2x2life Dec 03 '13 at 13:20
  • @DKal May i please get the answer to which i will get marks? I really want to know that I was the one with the highest marks in the world or the second highest! – Rachit Bhargava Dec 03 '13 at 14:50