Find the measure of the angles around point $P$, where $P$ is the intersection of three lines. We are given the measures of 6 angles around the intersection point $P$ as $58^{\circ}$, $65^{\circ}$, $25^{\circ}$, $100^{\circ}$, $60^{\circ}$, and an unknown angle, which we will call $x$. We need to find the value of $x$.

1. Problem Description

Find the measure of the angles around point $P$, where $P$ is the intersection of three lines. We are given the measures of 6 angles around the intersection point $P$ as $58^{\circ}$, $65^{\circ}$, $25^{\circ}$, $100^{\circ}$, $60^{\circ}$, and an unknown angle, which we will call $x$. We need to find the value of $x$.

2. Solution Steps

The sum of the angles around a point is $360^{\circ}$. Therefore, we can write the equation:

$58^{\circ} + 65^{\circ} + 25^{\circ} + 100^{\circ} + 60^{\circ} + x = 360^{\circ}$

Now, we can add the known angles together:

$58 + 65 + 25 + 100 + 60 = 308$

So the equation becomes:

$308^{\circ} + x = 360^{\circ}$

To find $x$, subtract $308^{\circ}$ from both sides of the equation:

$x = 360^{\circ} - 308^{\circ}$

$x = 52^{\circ}$

3. Final Answer

The unknown angle $x$ is $52^{\circ}$.