Question

7 directions - use the diagram below to find the following measures:
gn is the angle bisector of $angle mgo$.
write the equation:
$x =$
$angle mgn =$ degrees.
$angle ogn =$ degrees.
$angle mgo =$ degrees.
$5x-6$
$11x-42$

Explanation:

Step1: Set angles equal (bisector property)

$5x - 6 = 11x - 42$

Step2: Solve for x (isolate variable)

$-6 + 42 = 11x - 5x \\
36 = 6x \\
x = \frac{36}{6} = 6$

Step3: Calculate $\angle MGN$

$\angle MGN = 5(6) - 6 = 30 - 6 = 24$

Step4: Calculate $\angle OGN$

$\angle OGN = 11(6) - 42 = 66 - 42 = 24$

Step5: Calculate $\angle MGO$

$\angle MGO = 24 + 24 = 48$

Answer:

Write the equation: $5x - 6 = 11x - 42$
$x = 6$
$\angle MGN = 24$ degrees.
$\angle OGN = 24$ degrees.
$\angle MGO = 48$ degrees.