Answer :
Final answer:
To find the measure of L3, we use the fact that complementary angles add up to 90 degrees and supplementary angles add up to 180 degrees. We can solve for L3 by substituting the given value of L1 into the equations and solving for L2 first.
Explanation:
To find the measure of L3, we can use the fact that complementary angles add up to 90 degrees, and supplementary angles add up to 180 degrees. Since L1 and L2 are complementary angles, we know that L1 + L2 = 90 degrees. Since L2 and L3 are supplementary angles, we know that L2 + L3 = 180 degrees. Given that L1 = 45 degrees, we can substitute this value into the first equation:
L1 + L2 = 90 degrees
45 + L2 = 90 degrees
L2 = 90 - 45 degrees
L2 = 45 degrees
Now, we can substitute the value of L2 into the second equation:
L2 + L3 = 180 degrees
45 + L3 = 180 degrees
L3 = 180 - 45 degrees
L3 = 135 degrees
Therefore, the measure of L3 is 135 degrees.
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