Question

Find the value of angles $x$ and $y$ in the following Kite.

Answer 1

Hint: The given figure is a kite, The logic here is, in a Kite, one pair of opposite angles are equal, that is the non-vertex angles and also the adjacent sides of a vertex angle are equal in length. There is one more property that is very important to remember while solving the questions of kite or any quadrilateral, that is the angle sum property of quadrilaterals.

Complete step by step answer:
The given figure is a Kite as shown below:

We need to find the unknown angles $x$ and $y$. 

There is one pair of opposite angles that will be equal, that is non-vertex angles which are equal.
Therefore, $y = {110^ \circ }$
As they are the non-vertex angles of a Kite.
Now, We have to find the value of $x$.
As we know, There is one more property related to kite or any quadrilateral, that is the angle sum property, which states that the sum of all angles of a Quadrilateral is equal to $360^\circ$.
So,
${110^ \circ } + {60^ \circ } + y + x = {360^ \circ }$ (by angle sum property)
Now,
Put the value of $y = {110^ \circ }$
${110^ \circ } + {60^ \circ } + {110^ \circ } + x = {360^ \circ }$
On adding, we get
${280^ \circ } + x = {360^ \circ }$
$\Rightarrow x = {360^ \circ } - {280^ \circ }$
$\therefore x = {80^ \circ }$
Hence, the value of $x$ is ${80^ \circ }$ and the value of $y$ is ${110^ \circ }$. and the whole Kite figure with corresponding angles is shown below.

Note:
While solving problems related to quadrilaterals, one should know their basic properties. As it is given in the question that it is a kite. Therefore, kites possess a property that the diagonals of a kite intersect each other at ${90^ \circ }$ and the diagonals through the non-vertex angles bisect at the point of intersection.