Question

find the value of x,y and z.​

Answer 1

Answer:

in triangle ADC

A+D+C = 180

50⁰+90⁰+C = 180⁰

140⁰+C = 180⁰

C = 180⁰-140⁰

C = 40⁰

x = 90⁰

in triangle EBC

E+B+C = 180⁰

90⁰+y+40⁰ = 180⁰

150⁰+y = 180⁰

y = 180⁰-150⁰

y = 30⁰

E+D+O+C = 360⁰

90⁰+90⁰+O+40⁰ = 360⁰

180⁰+40⁰+O = 360⁰

220+O = 360⁰

O = 360⁰-220⁰

O = 140⁰

Z = O (V.O.A)

Z = 140⁰

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Answer 2

Step-by-step explanation:

in triangle AOE :

angle AOE = 180°-(50°+90°) = 40°

angle AOE = angle BOD = 40°

y+x+40 = 180 or x+y = 140° .....(1)

angle ABC = 2(angle EBC) = 2y

angle ABE = angle EBC = y

in triangle ABO:

y + z + angle ABO = 180

angle ABO = 180 - y - z. .....(2)

in triangle EBC :

angle ECB = 180-(90+y) = 90 - y

in quadrilateral OECD

EOD + ODC +DCE + CEO = 360

z + (180-x) + (90 - y) + 90 =360

z - x - y = 360 -180-90-90 = 0

z =x + y = 140. ( from eq 1)

in equation 3 :

angle ABC = 2y = z - y -50

2y + y = 140 - 50

3y = 90

y = 30

in equation 1 :

x+y =140

x = 140 -y = 140 - 30

x = 110