Question

what is the value of w?
12v - 3°
w - 38°
34v - 38°
15v
w = °
submit

Explanation:

Step1: Use exterior angle theorem

$\angle 34v-38^\circ = \angle 12v-3^\circ + \angle 15v$

Step2: Solve for $v$

$34v - 38 = 12v - 3 + 15v$
$34v - 38 = 27v - 3$
$34v - 27v = -3 + 38$
$7v = 35$
$v = 5$

Step3: Find adjacent angle measure

$\angle w-38^\circ = 180^\circ - (34v-38^\circ)$
Substitute $v=5$:
$\angle w-38^\circ = 180 - (34\times5 - 38)$
$\angle w-38^\circ = 180 - (170 - 38)$
$\angle w-38^\circ = 180 - 132$
$\angle w-38^\circ = 48^\circ$

Step4: Solve for $w$

$w - 38 = 48$
$w = 48 + 38$

Answer:

$86$