Question

1. ∠abd is an acute angle. what are the possible values for x? assume m∠abc cannot be 0°.

Explanation:

Step1: Define ∠ABD measure

$m\angle ABD = 3x + 18$

Step2: Set acute angle inequality

An acute angle is less than $90^\circ$, so:
$3x + 18 < 90$

Step3: Solve upper bound for x

Subtract 18, then divide by 3:
$3x < 90 - 18$
$3x < 72$
$x < 24$

Step4: Set positive angle constraint

Since $m\angle ABC
eq 0^\circ$, $3x > 0$:
$x > 0$

Answer:

$0 < x < 24$