Vertical angles are a pair of angles formed when two lines intersect. They are always congruent, meaning they have the same measure.
In this case, we are given that the measure of one vertical angle, L1, is (n + 13)°, and the measure of the other vertical angle, 23, is (4n + 4)°.
Since vertical angles are congruent, we can set up an equation to find the value of n. We have:
(n + 13)° = (4n + 4)°
To solve for n, let's simplify the equation:
n + 13 = 4n + 4
Subtract n from both sides:
13 = 3n + 4
Subtract 4 from both sides:
9 = 3n
Divide both sides by 3:
3 = n
Now that we have found the value of n, we can substitute it back into either angle measure to find the measure of each angle. Let's use L1:
L1 = (n + 13)°
L1 = (3 + 13)°
L1 = 16°
Therefore, the measure of each angle is 16°.
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Math 7B Unit 3 Study Guide
14. For two vertical angles with measures mL1 = (n + 13)° and m23 = (4n + 4)°, what is the measure of each angle?
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