Question

current skill $\
$ in triangle def, angle d is 54°, angle e is 63°, angle f is 6w + 9°. find the value of w and the measure of angle dfe (m∠dfe). $\
$ w = $\
$ m∠dfe =

Explanation:

Step1: Sum of angles in triangle

$54^\circ + 63^\circ + (6w + 9)^\circ = 180^\circ$

Step2: Simplify the equation

$126 + 6w = 180$

Step3: Solve for w

$6w = 54 \implies w = 9$ (Note: Correction—original calculation error: 54+63+9=126, 180-126=54, 54/6=9. Correct w=9)

Wait, revised correct steps:

Step1: Triangle angle sum

$54 + 63 + 6w + 9 = 180$

Step2: Combine constants

$126 + 6w = 180$

Step3: Isolate w term

$6w = 180 - 126 = 54$

Step4: Solve for w

$w = 54/6 = 9$

Final Answer: 9

Step1: Apply triangle angle sum

$54 + 63 + 6w + 9 = 180$

Step2: Combine like terms

$126 + 6w = 180$

Step3: Subtract 126 from both sides

$6w = 54$

Step4: Divide by 6

$w = 9$

Answer:

10