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The square ABCD above has a side length equal to 1. If ∠EAF = 45°, and 12 Oct 2020, 01:00
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The square ABCD above has a side length equal to 1. If ∠EAF = 45°, and ∠AFB = 70°. What is the measure of angle AEF?


A. 50°
B. 55°
C. 60°
D. 65°
E. 70°

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D
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The square ABCD above has a side length equal to 1. If ∠EAF = 45°, and Updated on: 19 Oct 2020, 01:14
Originally posted by QuantMadeEasy on 13 Oct 2020, 00:25.
Last edited by QuantMadeEasy on 19 Oct 2020, 01:14, edited 1 time in total.
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Quote:
The square ABCD above has a side length equal to 1. If ∠EAF = 45°, and ∠AFB = 70°. What is the measure of angle AEF?
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Step 1: Understanding the question
In ΔFBA, ∠BAF = 20°
As ∠BAD = 90, ∠EAD = 25° and ∠DEA = 65°

Refer to the attachment:
Lets form a ΔHAG such that ∠HAG = 45°, ∠BAH = ∠GAD = 22.5°, hence, AH = AG and ∠GHA = ∠AGH = 67.5

When G point coincides with E and H with F, ∠AEF is slightly less than 67.5

IMO D
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The square ABCD above has a side length equal to 1. If ∠EAF = 45°, and 13 Oct 2020, 00:59
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QuantMadeEasy
Quote:
The square ABCD above has a side length equal to 1. If ∠EAF = 45°, and ∠AFB = 70°. What is the measure of angle AEF?
Step 1: Understanding the question
In ΔFBA, ∠BAF = 20°
As ∠BAD = 90, ∠EAD = 25° and ∠DEA = 65°

Refer to the attachment:
Lets form a ΔHAG such that ∠HAG = 45°, ∠BAH = ∠GAD = 22.5°, hence, AH = AG and ∠GHA = ∠AGH = 67.5

When G point coincides with E and H with F, ∠AEF is greater than 67.5

IMO E
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sorry the answer is D by congruent triangles
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GMAT Focus 1: 735 Q90 V89 DI81
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The square ABCD above has a side length equal to 1. If ∠EAF = 45°, and 15 Oct 2020, 00:32
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QuantMadeEasy
Quote:
The square ABCD above has a side length equal to 1. If ∠EAF = 45°, and ∠AFB = 70°. What is the measure of angle AEF?
Step 1: Understanding the question
In ΔFBA, ∠BAF = 20°
As ∠BAD = 90, ∠EAD = 25° and ∠DEA = 65°

Refer to the attachment:
Lets form a ΔHAG such that ∠HAG = 45°, ∠BAH = ∠GAD = 22.5°, hence, AH = AG and ∠GHA = ∠AGH = 67.5

When G point coincides with E and H with F, ∠AEF is greater than 67.5

IMO E
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Rather it is opposite....∠AEF is smaller than 67.5
If the triangle were isosceles, that is AE=AF, then both ∠AEF and ∠AFE would be 67.5 each. But point F is closer to vertex as it makes a 70 degree angles as compared to point E, which makes 65.
Thus AE>AF, and the corresponding opposite angles will also have the same relation => ∠AEF < ∠AFE, so ∠AFE is greater than 67.5, while ∠AEF is smaller than 67.5
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The square ABCD above has a side length equal to 1. If ∠EAF = 45°, and 16 Oct 2020, 02:35
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quantmadeeasy i like your diagram you can also find angle aed i.e 65 now fold the page as given above you will get answer 65 hence D

Or another way if you look at the diagram it is shifted towards angle b side so between angle f and e angle and e has to be more by the property angle opposite to greater side is greater and we know that side FC is bigger so angle e has to be bigger even if we consider both of them equal it will be 45 degree(in real it will be little more)
we know that side is 180 degree from that angle aed is 65 degree and angle fec is 45 so angle aef will be 70 degree but we have considered angle fec a little less so the next lowest option is the correct answer i.e option d 65 degree



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