Find the value of the angles marked with letters in the following:

Part (a)

Step 1: The sum of the interior angles in a triangle is $180^\circ$.

$\angle 1 + \angle 2 + \angle 3 = 180^\circ$

Step 2: Label the given angles.

$\angle A = 18^\circ, \ \angle B = x^\circ, \ \angle C = 20^\circ$

Step 3: Substitute the known angles into the formula.

$18^\circ + x^\circ + 20^\circ = 180^\circ$

Step 4: Simplify the left side.

$38^\circ + x^\circ = 180^\circ$

Step 5: Subtract $38^\circ$ from both sides to isolate $x^\circ$.

$x^\circ = 180^\circ - 38^\circ$

Step 6: Calculate the difference.

$x^\circ = 142^\circ$

x = 142^\circ

Part (b)

Step 1: Adjacent angles on a straight line sum to $180^\circ$.

$\angle adjacent = 180^\circ - given\ angle$

Step 2: The given angle is $130^\circ$.

$b^\circ = 180^\circ - 130^\circ$

Step 3: Calculate the difference.

$b^\circ = 50^\circ$

b = 50^\circ