Question

find the values of x and y in the following figures ​

Answer 1

Answer:

Step-by-step explanation:

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If one side of a triangle is produced,

then the exterior angle thus formed

is equal to the sum of the two interior

opposite angles.

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i ) In ∆ABC ,

<B + <C = Exterior angle at A

x + 57° = 107°

=> x = 107° - 57°

=> x = 50°

ii) In ∆ADC ,

a ) Exterior angle DCE = <A + <ADC

y + 65° = 40° + 107°

=> y = 147° - 65°

y = 82°

b) <ACE = 180° [ straight angle ]

x° + 65° + y° = 180°

=> x° + 65° + 82° = 180°

=> x° + 147° = 180°

x° = 180° - 147°

x° = 33°

Therefore,

x° = 33° ,

y = 82°

••••

Answer 2

Answer:

∠CAB=80

o

[apposite angle]

as AB=AC

x=∠ACB

⇒x+x+80=180

2x=100

x=50

y=80+x=130 exterior angle property

x=50