Question

find x if m∠hgs = 3x + 5, m∠sgf = 21x + 3, and m∠hgf = 176°. options: x = 7°, x = 12°, x = 144°, x = 6°

Explanation:

Step1: Set up angle sum equation

$\angle HGS + \angle SGF = \angle HGF$

Step2: Substitute given expressions

$3x + 5 + 21x + 3 = 176$

Step3: Combine like terms

$24x + 8 = 176$

Step4: Isolate variable term

$24x = 176 - 8$
$24x = 168$

Step5: Solve for x

$x = \frac{168}{24}$

Answer:

$x = 7^\circ$