Answer:
see explanation
Explanation:
(a)
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles
w is the exterior angle of the upper triangle , then
w = a + c → (1)
y is the exterior angle of the lower triangle , then
y = b + d → (2)
add (1) and (2)
w + y = a + c + b + d , that is
w + y = a + b + c + d
(b)
the exterior angle + interior angle = 180° , so
exterior angle = 180° - interior angle
w, x, y and z are exterior angles of the quadrilateral
x = 180° - c + d) = 180° - c - d
z = 180° - (a + b) = 180° - a - b
Then using these results combined with (1) and (2) from part (a)
w + x + y + z
= a + c + 180° - c - d + b + d + 180° - a - b ( collect like terms )
= 360°
then w + x + y + z = 360°