Question

find the measure of ∠lon.

Explanation:

Step1: Recall angle - sum property of a full - turn

The sum of angles around a point is 360°.

Step2: Set up the equation

Let $\angle LON=x$. We know that $x + 48^{\circ}+84^{\circ}+ 90^{\circ}=360^{\circ}$ (assuming the un - labeled angle is a right - angle, since the figure seems to suggest a 90 - degree angle at the bottom - left corner).

Step3: Simplify the left - hand side

$x+(48 + 84+90)^{\circ}=360^{\circ}$, so $x + 222^{\circ}=360^{\circ}$.

Step4: Solve for $x$

Subtract 222° from both sides: $x=360^{\circ}-222^{\circ}$.
$x = 138^{\circ}$

Answer:

$138^{\circ}$