Question

35. In the figure ZACE = 36°, 2CAE = 41°. Find x, y and z.​

Answer 1

Answer:

since the sum of opposite angles of a cyclic quadrilateral is 180 deg.

therefore

x + 41 = 180

x = 180 - 41

x = 139

sum of the angles made on the one side of straight line is 180 deg

therefore

x + y =180

139 + y =180

y = 180-139

y = 41

now in the triangle CAE;

∠CEF is an external angle

therefore ∠CEF=∠ACE+∠CAE

external angle of a triangle is equal to the sum of two opposite angles

∠CEF=36+41=77

and in triangle DEF ;y+∠DEF+z=180

[sum of interior angles of a triangles]

z=180−(y+∠DEF)

z=180−(41+∠CEF)

z=180−(41+77)

z=180−118

z=62