Bang bang

Geometry Level 2

In A B C \triangle ABC , A D B D AD \perp BD at point D D , B E A C BE \perp AC at point E E , A D AD and B E BE intersects at F F , if B F = A C BF = AC , find the measure of A B C \angle ABC in degrees.

Note : Figure not drawn up to scale.

45 40 50 35

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4 solutions

Aniket Verma
Mar 2, 2015

In actual D D , F F and E E conside C C and since B F = A C BF = AC , so the the triangle is a right angled isosceles triangle with C = 9 0 o \angle C = 90^{o} and other two angles = = 4 5 o 45^{o} .

therefore A B C = 4 5 o \angle ABC=45^{o}

Ahmed Moh AbuBakr
Mar 28, 2015

Sin(BFD)=sin(ACD) SO BD/BF =AD/AC BF GOING WITH AC BF BECAUSE BF=AC SO BD =AD THEN (Abd)=45

Hansen Young
Apr 30, 2015

Since BF = AC

and BDF = ADC,

therefore we can conclude that AD=BD

thus, triangle ACD and BDF are congruent (SAS)

In triangle ABD, if ADB is 90 and the other 2 sides are of same length, therefore it's an isosceles triangle

Measure of ABD = (180-90)/2

                                = 45
Guru Prasaadh
Apr 3, 2015

question was for 45 points and i entered 45. just kidding ,look at the picture carefully you will notice that 45degree is the only possible angle that can be formed

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