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Bunuel

In the figure above, ABC is right angled triangle at B and EF⊥CA. What is the measure of ∠AEC, if ∠ADB = 55°?

(A) 180°
(B) 135°
(C) 125°
(D) 55°
(E) 35°

Attachment:
2021-03-09_20-21-13.png

Answer: Option D

Relevant CONCEPT: Triangle altitudes are concurrent



PROOF

Video solution by GMATinsight



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Hi GMATinsight,

I saw your video, great explanation. I am aware that the 3 altitudes of a triangle are concurrent. However, I am not able to understand that how extension from D to G, DG, or AG, can be called as a perpendicular to side EC of triangle AEC. Can you please clarify this, if possible?
TIA.

Regards,
Ravish.

ravish844

Because CB and EF are perpendiculars (altitudes) passing through point D

So third altitude starting from point A must also pass through D hence, AD is a part of altitude AG.
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GMATinsight

Relevant CONCEPT: Triangle altitudes are concurrent



PROOF

Video solution by GMATinsight



Two MUST join YouTube channels for GMAT aspirant GMATinsight (1000+ FREE Videos) and GMATclub :)
For a Comprehensive Topicwise Quant Video course at an affordable price CLICK HERE


Hi GMATinsight,

I saw your video, great explanation. I am aware that the 3 altitudes of a triangle are concurrent. However, I am not able to understand that how extension from D to G, DG, or AG, can be called as a perpendicular to side EC of triangle AEC. Can you please clarify this, if possible?
TIA.

Regards,
Ravish.

ravish844

Because CB and EF are perpendiculars (altitudes) passing through point D

So third altitude starting from point A must also pass through D hence, AD is a part of altitude AG.

Hi GMATinsight,

Thanks a lot for your reply. Now, it's clear to me.
Thanks once again for an excellent explanation in this video.

Regards,
Ravish.
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