Question

what is the value of b?
$x + 48^{circ}$
$12b + 50^{circ}$
$30^{circ}$
$4x - 48^{circ}$
$b = \square^{circ}$
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Explanation:

Step1: Use exterior angle theorem

$x + 48^\circ = 30^\circ + 4x - 48^\circ$

Step2: Solve for $x$

$x - 4x = 30^\circ - 48^\circ - 48^\circ$
$-3x = -66^\circ$
$x = 22^\circ$

Step3: Find adjacent angle to $x+48^\circ$

The angle supplementary to $x+48^\circ$ is $180^\circ - (22^\circ + 48^\circ) = 110^\circ$

Step4: Use triangle angle sum

$110^\circ + 30^\circ + 12b + 50^\circ = 180^\circ$

Step5: Simplify and solve for $b$

$12b + 190^\circ = 180^\circ$
$12b = -10^\circ$
Correction: Use exterior angle for $12b+50^\circ$

Step1 (Revised): Use exterior angle for $x+48$

$x + 48 = 30 + 4x - 48$
$x - 4x = 30 - 96$
$-3x = -66$
$x = 22$

Step2: Find $12b+50$ via exterior angle

$12b + 50 = 30 + (x + 48)$

Step3: Substitute $x=22$

$12b + 50 = 30 + 22 + 48$
$12b + 50 = 100$

Step4: Solve for $b$

$12b = 100 - 50$
$12b = 50$
$b = \frac{50}{12} = \frac{25}{6}$

Answer:

$\boldsymbol{\frac{25}{6}}$ or $\boldsymbol{4\frac{1}{6}}$