Question

the figure ABCDis 11 gm .find angle measure X,Y,Z state the Property​

Answer 1

Let ABCD is a convex quadrilateral, then we draw a diagonal AC which divides the quadrilateral in two triangles.

Ð A + ÐB + Ð C + Ð D = Ð 1 + Ð 6 + Ð 5 + Ð 4 + Ð 3 + Ð 2

Ð A + ÐB + Ð C + Ð D = Ð 1 + Ð 6 + Ð 5 + Ð 4 + Ð 3 + Ð 2 = (Ð 1 + Ð 2 + Ð 3) + (Ð 4 + Ð 5 + Ð 6)

Ð A + ÐB + Ð C + Ð D = Ð 1 + Ð 6 + Ð 5 + Ð 4 + Ð 3 + Ð 2 = (Ð 1 + Ð 2 + Ð 3) + (Ð 4 + Ð 5 + Ð 6)= 1800 + 1800 [By Angle sum property of triangle]

Ð A + ÐB + Ð C + Ð D = Ð 1 + Ð 6 + Ð 5 + Ð 4 + Ð 3 + Ð 2 = (Ð 1 + Ð 2 + Ð 3) + (Ð 4 + Ð 5 + Ð 6)= 1800 + 1800 [By Angle sum property of triangle]= 3600

Ð A + ÐB + Ð C + Ð D = Ð 1 + Ð 6 + Ð 5 + Ð 4 + Ð 3 + Ð 2 = (Ð 1 + Ð 2 + Ð 3) + (Ð 4 + Ð 5 + Ð 6)= 1800 + 1800 [By Angle sum property of triangle]= 3600Hence, the sum of measures of the triangles of a convex quadrilateral is 3600.

Ð A + ÐB + Ð C + Ð D = Ð 1 + Ð 6 + Ð 5 + Ð 4 + Ð 3 + Ð 2 = (Ð 1 + Ð 2 + Ð 3) + (Ð 4 + Ð 5 + Ð 6)= 1800 + 1800 [By Angle sum property of triangle]= 3600Hence, the sum of measures of the triangles of a convex quadrilateral is 3600.Yes, if quadrilateral is not convex then, this property will also be applied.

Answer 2

Answer:

y = 30° ( opposite angle is equal)

angle b = 180- 60 = 130° ( linear line)

x= 130° ( opposite angle is equal)