Question

in the given figure AB||CD. find the angles x,y,z​

Answer 1

Answer:

X+90+30 =180(angle sum property)

x+ 120 = 180

x= 180-120

x= 20

y+x+80 =180(linear pair)

y+20+80=180

y=180-100

y=80

z=x (alternative angles and AB parallel to CD)

z=20

Step-by-step explanation:

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Answer 2

$\rm{\angle ECF + \angle CEF + \angle EFC = 180^\circ\quad...\:By\:Angle\:Sum\:Property\:in\:\triangle CEF}$

$\longrightarrow\rm{90^\circ + 30^\circ + x = 180^\circ}\longrightarrow\rm{120^\circ + x = 180^\circ}\longrightarrow\rm{x = 180^\circ-120^\circ}\longrightarrow\rm{x = 60^\circ}$

$\rm{\angle EFC+\angle AFE+80^\circ=180^\circ\quad...\:Straight \:Line \:Angle\: Property}$

$\longrightarrow\rm{x+y+80^\circ=180^\circ}\longrightarrow\rm{60^\circ+y+80^\circ=180^\circ}$

$\longrightarrow\rm{140^\circ+y=180^\circ}\longrightarrow\rm{y=180^\circ-140^\circ}\longrightarrow\rm{y=40^\circ}$

$\rm{\angle BAF = \angle EFC + \angle AFE}\longrightarrow\rm{z = x+y}\longrightarrow\rm{z = 60^\circ+40^\circ}\longrightarrow\rm{z = 100^\circ}$