Question

in the given figure . angle DCA =60 DEGREE .Angle ECD = 30 degree . find x ,y ,z. give proper reasons

Answer 1

angle z + 60+30=180° ( angle sum property )
angle z= 90°
if the line that is forming the 30° ( not the base ) is parralel to the hypotenuse of the triangle . angle 60° = angle y ( alternate angle )
angle z+90(z)+60(y) = 180° ( angle sum property )
angle z = 30°

Answer 2

Angle z = 60 + 30 = 90. and. 180 - 90. = 90 ( 60 and 30 are exterior angle on 180 degree ). so angle z = 90. Angle y is alternate to 60 degree exterior angle. so angle y = 60. Angle x = z + y - 180. ................Angle x = 90 + 60 -180..............Angle x. = 150 - 180. means angle x = 30 degree. so. z= 90. y = 60. x= 30