Question

Find the value of x shown in the picture.

Answer 1

`\sf\\(i)\ \angle F=\angle H=(x+5)^o\ \ \ [\textsf{The opposite angles formed by meeting of two}\\\textsf{pairs of non-congruent sides in a kite are equal.]}\\\\(ii)\ \angle E+\angle F+\angle G+\angle H=360^o\ \ \ [\textsf{Sum of interior angles of quadrilateral is 180}^o.]\\or,\ x+x+5^o+140^o-x+x+5^o=360^o\\or,\ 2x+150^o=360^o\\or,\ 2x=210^o\\or,\ x=105^o`

Alternatively, you may also solve this question by joining the points F and H, and then use the theorem of isosceles triangles.