Question

in the given pattern eight isocseles trapeziums sorround a regular . what is the measure of angle Z in trapezium WXYZ

Answer 1

Answer:

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Answer 2

Question:-

in the given pattern eight isocseles trapeziums sorround a regular . what is the measure of angle Z in trapezium WXYZ

$\huge \boxed{ \bf \: solution}$

Let , WXYZ be ABCD ( B = Z)

n(exactly one )

n( A- x( a Ω b )-[ n(a Ω c)-n(a Ω b Ω c)]

+n(b)-n(a Ω b)-n(a Ω b Ω c)]

+n(c)-n(a Ω c)-[n(b Ω c)-n(a Ω b Ω c)]

=> n(a)+n(b)+n(c)-2n(a Ω b)-2n(b Ω c)

-2n(c Ω a)+3n(a Ω b Ω c)

=>40+30+20-20-18-16+9 = 99-54 = 45

Answer => 45

$\mathtt{{\colorbox{silver}{second \: way \: to \: solve \: this \: question \: }}}</p><p>$

let WXYZ = ABCD ( optional )

$\angle \sf \: pcv = 135 \degree$

(internal angle of a regular octagon)

$\angle \sf \: dcv = 180 \degree \: - \angle \: pcv = 180 \degree \: - 135 \degree \: = 45 \degree$

(PCD is a straight line )

$\therefore \angle \sf \: b = \angle \: dcv \: = 45 \degree \\ \sf \: (properties \: of \: isosceles \: triangle \: )$