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Which one of the following relations is true regarding the angles of

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Bunuel
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Which one of the following relations is true regarding the angles of [#permalink] New post  03 Apr 2019, 23:06
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Which one of the following relations is true regarding the angles of the quadrilateral shown in figure?

(A) \(∠A = ∠C\)

(B) \(∠B > ∠D\)

(C) \(∠A < ∠C\)

(D) \(∠B = ∠D\)

(E) \(∠A = ∠B\)


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Which one of the following relations is true regarding the angles of [#permalink] New post  06 Apr 2019, 00:41
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Beautiful question.

I would like to take this up.

Firstly, let’s join AC.

Now, In triangle ABC,
Side BC > Side AB
Thus, Angle CAB > angle BCA ...........(1)

——Cause Angle opposite to a larger side is larger.——

In triangle ADC,
Side CD > Side AD
Thus, Angle CAD > angle ACD ..........(2)

From (1) & (2)
Angle CAB + Angle CAD > angle BCA + angle ACD
i.e. Angle A > Angle C

Following the same logic, we construct BD and prove that
Angle B > angle D.

Hence, option B is the correct answer.

Kudos please if you liked the answer
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smita123
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Re: Which one of the following relations is true regarding the angles of [#permalink] New post  04 Apr 2019, 12:31
The image is of quadrilateral which has two lines parallel to each other.

Option A, D and E are completely irrelevant coz there is no relation that those angles can be equal.

In between option B and C, B can be logically correct.

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stne
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Which one of the following relations is true regarding the angles of [#permalink] New post  05 Apr 2019, 12:55
smita123 wrote:
The image is of quadrilateral which has two lines parallel to each other.

Option A, D and E are completely irrelevant coz there is no relation that those angles can be equal.

In between option B and C, B can be logically correct.

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Hi smita123,
Can you clarify, which two lines are you considering parallel to one another and how?
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Re: Which one of the following relations is true regarding the angles of [#permalink] New post  06 Apr 2019, 00:14
Sorry, i did wrong interpretation. Thanks for pointing out.

Well i dont know the explanation then.

Can anyone explain why B is right?

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Re: Which one of the following relations is true regarding the angles of [#permalink] New post  08 Oct 2020, 10:01
I seemingly have a misconception. Drawing a line from B to D, I now have two large triangles Both, Angle C and Angle A, are opposite angles to the same hypothenuse BD. Already feeling that this would be too easy I thought that Angle A = Angle C.

Why doesn't this hold true?
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stne
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Re: Which one of the following relations is true regarding the angles of [#permalink] New post  08 Oct 2020, 10:08
Bunuel wrote:

Which one of the following relations is true regarding the angles of the quadrilateral shown in figure?

(A) \(∠A = ∠C\)

(B) \(∠B > ∠D\)

(C) \(∠A < ∠C\)

(D) \(∠B = ∠D\)

(E) \(∠A = ∠B\)


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Hope it's clear.
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Re: Which one of the following relations is true regarding the angles of [#permalink]
08 Oct 2020, 10:08
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