To find the measure of UFK, we need to use the fact that supplementary angles add up to 180 degrees.
We have mUFK = 2n° and m<KFL = (3n + 30)°.
Since these angles are supplementary, their measures add up to 180 degrees:
2n + (3n + 30) = 180.
Simplifying the equation, we have:
2n + 3n + 30 = 180.
Combining like terms:
5n + 30 = 180.
Subtracting 30 from both sides:
5n = 150.
Dividing both sides by 5:
n = 30.
Now we can find the measure of UFK using the value of n:
mUFK = 2n = 2(30) = 60°.
Therefore, the measure of UFK is 60°.
The correct answer is C) 60°.
Math 7B Unit 3 Study Guide
10. Two angles are supplementary with measures mUFK = 2n° and
m<KFL = (3n + 30)". What is the measure of UFK?
A) 180°
B) 90°
C) 60°
D) 24°
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