खालील समभुज त्रिकोणांचे अतिव्यापन दर्शविणारी आकृती अभ्यासा आणि कोन a चे अंशामधील मूल्य निवडा.

The correct answer is Option 1 [49].

Geometric Step-by-Step Proof:

The triangles given in the figure are equilateral triangles. Therefore, each interior angle of an equilateral triangle measures exactly $60^\circ$.

1. Angles on a Straight Line (Linear Pair Theorem):

   • At the first intersection, the straight line consists of the angle $72^\circ$, the equilateral triangle angle ($60^\circ$), and angle $q$:
     

     $$q = 180^\circ - (72^\circ + 60^\circ) = 180^\circ - 132^\circ = 48^\circ$$

2. At the second intersection:

   • The line consists of angle $59^\circ$, the equilateral triangle angle ($60^\circ$), and angle $r$:
     

     $$r = 180^\circ - (59^\circ + 60^\circ) = 180^\circ - 119^\circ = 61^\circ$$

3. Angle Sum Property of the intermediate central triangle:

   • Let the third angle of this triangle be $s$:
     

     $$s = 180^\circ - (q + r) = 180^\circ - (48^\circ + 61^\circ) = 180^\circ - 109^\circ = 71^\circ$$

4. Calculating angle $a$:

   • From the adjacent geometry where angle $a$ is formed with angle $s$ and the $60^\circ$ equilateral triangle angle:
     

     $$a = 180^\circ - (s + 60^\circ) = 180^\circ - (71^\circ + 60^\circ) = 180^\circ - 131^\circ = 49^\circ$$

Therefore, the value of angle $a$ is $49^\circ$.