The perimeter of a certain sector of a circle is equal to the length of the arc of  semi circle having the same radius. Express the angle of the sector in degrees, minutes and seconds.

Explanation

To solve the problem, we need to find the angle of a sector of a circle given that its perimeter is equal to the length of the arc of a semicircle with the same radius.

### Step 1: Define the variables
Let the radius of the circle be \( r \) and the angle of the sector be \( \theta \) (in radians).

### Step 2: Calculate the perimeter of the sector
The perimeter \( P \) of the sector consists of the two radii and the arc length. The arc length \( L \) of the sector is given by:
\[
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