# find the values of w, x, y and z                                                    /...

find the values of w, x, y and z

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/54 degrees

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/  y (corner of triangle)

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/ x (corner of triangle)      46 degrees (corner of triangle)

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w degrees

The triangle forms from below y to the corner of 46 degrees then back to the corner of x/w.  I straight line slants

through the dotted/slanted lines.

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/

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/32 degrees  (the corner of the triangle)

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/z degrees(this line goes thru the triangle)

this is the corner of the triangle

I hope this make sense

The top diagram forms a backward Z shape with a slanted line going down the left side connecting the corner of the Y degrees and 54 degrees to the corner of x degrees and w degrees.

The bottom diagram is an acute angle with a 32 degreee angle.  Then a line goes through the bottom of the open angle forming an abtuse angle that is z degrees.

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ajju | Certified Educator

i draw the figure using given content.

here ab and cd are parallel lines and line bc intersecting them.

then angle bcd = angle abc

then angle abc = 46.

the angle sum on a line at one point = 180

then angle abe + angle abc + angle cbd = 180

or 54 + 46 + y = 180

100 + y = 180

y = 180 - 100 = 80

Angles bcd , cbd, bdc are the internal angles of triangle bcd.

the angle sum of triangle = 180

then Angle bcd + angle cbd + angle bdc = 180

46 + 80 + x = 180

126 + x = 180

x = 180 - 126 = 54.

and angle w is the obtuse angle of x

the angle w = 180 - 54 = 126.

and angle z = 180 - 32 = 148.

i have little of confusion in bottom figure. so if u have any doubt or want to any other explanation please send me a well defined figure in paint or other tool.

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