abcd is a rectangle, e is the point on bc and f is the point on cd, if angle fae is equal to 45 degree and angle aeb is equal to 70 degree then find angle afe
Answers
The
Step-by-step explanation:
The Angle AFE=65degrees
Given : ABCD is a rectangle, E is the point on BC and F is the point on CD, ∠FAE is equal to 45° and AEB is equal to 70°
To Find :∠AFE
Solution:
Assume square is of 1 unit side
∠AEB = 70°
=> ∠BAE = 20°
=> ∠DAF = 25° ( 90° - 20° - 45° )
=> AFD = 65°
Tan25° = FD/AD
=> FD = Tan 25°
=> CF = 1 - tan25°
Tan 20° = BE/AB
=> BE = tan 20°
=> CE = 1 - tan 20°
tan ∠CFE = CE/CF
( 1 - tan 20°)/( 1 - tan25° )
tan20° = tan (45° - 25°) = ( 1 - tan25°) /( 1 +tan25°)
1 - tan20° = 1 - ( 1 - tan25° /( 1+tan25°)
= 2 tan25° /( 1 + tan25°)
tan ∠CEF = 2 tan25°/( 1 + tan25°) ( 1 - tan25° )
=> tan ∠CEF = 2 tan25°/( 1 + sin25°/cos25°) ( 1 - sin25°/cos25° )
=> tan ∠CEF = 2 cos25° . cos25°tan25°/( cos25° + sin25° ) ( cos25°- sin25° )
=> tan ∠CEF = 2 cos25° . Sin25°/( cos²25° -sin²25° )
=> tan ∠CEF = Sin50°/( Cos50° )
=> tan ∠CEF = tan50°
=> ∠CEF = 50°
∠AFE + ∠AFD + ∠CFE = 180°
=> ∠AFE + 65° + 50° = 180°
=> ∠AFE = 65°
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