We need to calculate the value of $x$ given the angles around a point on a straight line. The angles are $176^\circ$, $x$, $2x$, and $17^\circ$.

1. Problem Description

We need to calculate the value of $x$ given the angles around a point on a straight line. The angles are $176^\circ$, $x$, $2x$, and $17^\circ$.

2. Solution Steps

The angles on one side of a straight line add up to $180^\circ$. Therefore, the angles $x$, $2x$, and $17^\circ$ plus the $176^\circ$ angle should add up to $360^\circ$.

Alternatively, $x + 2x + 17 = 180 - 176 + 180 = 4 + 180 = 184$ because the angle subtended by the line is $180^\circ$

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

$x + 2x + 17^\circ + 176^\circ = 360^\circ$

Combine the terms with $x$:

$3x + 17^\circ + 176^\circ = 360^\circ$

Combine the constant terms:

$3x + 193^\circ = 360^\circ$

Subtract $193^\circ$ from both sides:

$3x = 360^\circ - 193^\circ$

$3x = 167^\circ$

Divide both sides by 3:

$x = \frac{167^\circ}{3}$

$x = 55.666...^\circ$ or $55\frac{2}{3}^\circ$

The sum of the angles on one side of the straight line is $180^\circ$, thus

$x+2x+17 = 180 - 176$ is wrong. It should be

$x + 2x + 17 = 184$, no degree here. This means $3x = 167$, and $x = 167/3$.

3. Final Answer

$x = \frac{167}{3}$