Question

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

Answer 1

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°