In the adjacent figure, B of Triangle ABC is a right angle. D, E, F are points on AB, AC and BC respectively such that AD = AE, CE = CF. Compute "Angle DEF".

Question

In the adjacent figure, B of Triangle ABC is a right angle D, E, F
are points on AB, AC and BC respectively such that AD = AE, CE = CF
Compute "Angle DEF"

Brijendra Pal · Accepted Answer

Hi,
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5a6cb235920e2%20png"
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Here angle B = 90 since in a triangle sum of all angles in a triangle is 180 soso angle A+angle C = 90
1 now AD = AE so angle ADE = angle AED Also CE = CF so angle CEF = angle CFE so in triangle ADE and CEF, angle A+∠1+∠1= 180 angle C +∠2+∠2= 180 adding both we get  angle A+angle C+2∠1+∠2= 360 using equation1 90+2∠1+∠2= 360 ∠1+∠2=  135
2now angle 1 angle 2 and angle DEF are forming linear pair so ∠1+∠2+angle DEF= 180 angle DEF= 180 -135 = 45 degree  using equation 2