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Question Number 140138 by henderson last updated on 04/May/21

Answered by mr W last updated on 04/May/21

Commented by mr W last updated on 04/May/21

yellow angle x=α+β+90°

yellowanglex=α+β+90°

Commented by mr W last updated on 04/May/21

Method I:

MethodI:

Commented by mr W last updated on 04/May/21

Commented by mr W last updated on 04/May/21

it can be easily proved that the red triangle is an isosceles right− angled triangle, therefore α+β=45° ⇒x=α+β+90°=135°

itcanbeeasilyprovedthattheredtriangleisanisoscelesright−angledtriangle,thereforeα+β=45°⇒x=α+β+90°=135°

Commented by mr W last updated on 04/May/21

Method II: tan α=((a−b)/(a+b)) tan β=(b/a) tan (α+β)=((((a−b)/(a+b))+(b/a))/(1−((a−b)/(a+b))×(b/a))) =((a^2 −ab+ab+b^2 )/(a^2 +ab−ab+b^2 ))=((a^2 +b^2 )/(a^2 +b^2 ))=1 ⇒α+β=45° ⇒x=α+β+90°=135°

MethodII:tanα=a−ba+btanβ=batan(α+β)=a−ba+b+ba1−a−ba+b×ba=a2−ab+ab+b2a2+ab−ab+b2=a2+b2a2+b2=1⇒α+β=45°⇒x=α+β+90°=135°

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