Question

Find the value of $x$ in the following figure.

Answer 1

Step 1. Analyze the given figure.

From the figure, we can say that $\angle Lmp=x$

$\angle LPN={96}^o$

$\angle mLP=3x$

$\angle LPN+\angle LPm={180}^o$ (because $\angle LPN$and $\angle LPm$ are linear pair angles).

$\angle LPm+{96}^o={180}^o$

$\angle LPm={180}^0-{96}^o$

$\angle LPm={84}^o$

Step 2. Find the value of x by applying the angle sum property of the triangle.

According to the angle sum property of the triangle.

In $△LPm$, $\angle mLP+\angle LPm+\angle LmP={180}^o$.

So put the value of all given angles.

$\angle mLP+\angle LPm+\angle LmP={180}^o$

$3x+{84}^o+x={180}^o$

$4x={180}^o-{84}^o$

$4x={96}^o$

$x=\frac{{96}^o}{4}$

$x={24}^o$

Hence, the value of $x$ is ${24}^o$.