Question

given ( mangle aoe = (2x + 72)^circ ) and ( mangle eod = (4x + 90)^circ ), find ( x ).

Explanation:

Step1: Identify supplementary angles

$\angle AOE$ and $\angle EOD$ form a straight line, so they are supplementary: $m\angle AOE + m\angle EOD = 180^\circ$

Step2: Substitute given expressions

$(2x + 72) + (4x + 90) = 180$

Step3: Combine like terms

$6x + 162 = 180$

Step4: Isolate the variable term

$6x = 180 - 162$
$6x = 18$

Step5: Solve for x

$x = \frac{18}{6}$

Answer:

$x = 3$