Question

find the value of x.
there is a diagram with lines intersecting at point g. one angle is 123°, and two angles are (x - 1)°. we need to find x.
x = \boxed{}

Explanation:

Step1: Identify supplementary angle

$\angle BGC = 180^\circ - 123^\circ = 57^\circ$

Step2: Set up angle sum equation

$\angle BGC + (x-1)^\circ + (x-1)^\circ + (x-1)^\circ = 180^\circ$

Step3: Simplify the equation

$57 + 3(x-1) = 180$
$57 + 3x - 3 = 180$
$3x + 54 = 180$

Step4: Solve for x

$3x = 180 - 54$
$3x = 126$
$x = \frac{126}{3} = 42$

Answer:

$42$