Question

In the given figure, what is z in terms of x and y?

Options

• x + y + 180

•  x + y − 180

• 180° − (x + y) 

•  x + y + 360°

Answer 1

In the given ΔABC, we need to convert z in terms of x and y 

Now, BC is a straight line, so using the property, “angles forming a linear pair are supplementary”

∠ABC + y = 180

∠ABC =180° - y°

Similarly,

∠ACB + x° = 180°

∠ACB = 180° - x

Also, using the property, “vertically opposite angles are equal”, we get,

 z = ∠BAC

Further, using angle sum property of the triangle

∠BAC + ∠ABC + ∠ACB = 180°

z° + (180°- y°) + (180° - x°) = 180°

              360° + z° - y° - x° = 180°

                        180° + z° = y° + x°

                                  z° = y°+ x° -180°

Thus,  z = y + x -180°