Question

In the above figure, both $RISK$ and $CLUE$ are parallelograms. Find the value of $x$.

Answer 1

Step 1: Apply properties of adjacent angles

From the given figure we can see that

$\angle K+\angle R=180°$ [$\because$adjacent angles of a parallelogram $=180°$]

Substituting $\angle K$ from the figure we get

$120°+\angle R=180°$

$\Rightarrow \angle R=180°–120°$

$=60°$

Step 2: Apply properties of corresponding angles

Again, $\angle KRI=\angle SIL$ [$\because$corresponding angles of a parallelogram are equal]

Substituting the value of $\angle KRI$ we get

$\angle SIL=60°$

Again, $\angle ECR=\angle ULC$ [$\because$corresponding angles of a parallelogram are equal]

Substituting the value of $\angle ULC$ from the figure we get

$\angle ECR=70°$

Step 3: Calculate $x$

Let the center point of the intersecting parallelograms be $O$

$\therefore \angle EOS=\angle IOC$ [$\because$verticle angles of a parallelogram are equal]

Substituting the value of $\angle EOS$ from the figure we get

$\angle IOC=x$

$\therefore$In $△IOC$ we get

$x+60°+70°=180°$ [$\because$sum of the angles of a triangle $=180°$]

$\Rightarrow$ $x+130°=180°$

$\Rightarrow$ $x=180°–130°$

$\Rightarrow$ $x=50°$

Hence, the value of $x$ from the given figure is $50°$.