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

1.	In the following figures, find the values of x and y.
Answer» In ΔABC, 107° = x° + 57° (exterior angle property) ∴ x° = 107° – 57° =50° In ΔADC, ∠CAD + ∠ADC + ∠ACD = 180° (angle – sum property) 40° + 107°+ x°= 180° ∴ x° = 180° – 147° = 33° Also in ΔABC, ∠A +∠B +∠C = 180° 40° + ∠B + (33° + 65°) = 180° ∠B + 138° = 180° B = 180° – 138° = 42° Now y° = ∠A + ∠B for ΔABC (exterior angle property) =40° + 42° = 82°

Answer»

In ΔABC,

107° = x° + 57° (exterior angle property)

∴ x° = 107° – 57° =50° In ΔADC,

∠CAD + ∠ADC + ∠ACD = 180° (angle – sum property)

40° + 107°+ x°= 180°

∴ x° = 180° – 147° = 33°

Also in ΔABC,

∠A +∠B +∠C = 180°

40° + ∠B + (33° + 65°) = 180°

∠B + 138° = 180°

B = 180° – 138° = 42°

Now y° = ∠A + ∠B for ΔABC (exterior angle property)

=40° + 42° = 82°

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