Question

In the following figures, find the values of x and y.

Answer 1

1)X= 107-57= 50°
2)X = 180-147= 33

Answer 2

Solution :

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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°

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