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# Find measures of complementary, supplementary, vertical, and adjacent angles

$\angle\;A$ and $\angle\;B$ are complementary angles. If $\angle\;A=50^o$, find the measure of $\angle\;B$.

Because $\angle\;A$ and $\angle\;B$ are complementary angles, $\angle\;A\;+\;\angle\;B=90^o$. Substituting 50º for $\angle\;A$ gives

$50^o\;+\;\angle\;B=90^o$.

Subtracting 50º from both sides, we find that $\;\angle\;B=90^o-50^o=40^o$.

$\angle\;A$ and $\angle\;B$ are supplementary angles. If $\angle\;A=125^o$, find the measure of $\angle\;B$.

Because $\angle\;A$ and $\angle\;B$ are supplementary angles, $\angle\;A\;+\;\angle\;B=180^o$. Substituting 125º for $\angle\;A$ gives

$125^o\;+\;\angle\;B=180^o$.

Subtracting 125º from both sides, we find that $\;\angle\;B=180^o-125^o=55^o$.

Determine the measures of $\angle\;2,\;\angle\;3,\;and\;\angle\;4$

Because vertical angles are equal, $\angle\;4=120^o$.

Because adjacent angles add up to 180º, then $\angle\;3\;+\;\angle\;4=180^o$. We also know $\angle\;4=120^o$. Substituting gives

$\angle\;3\;+\;120^o=180^o$.

Subtracting 120º from both sides, we find $\angle\;3=60^o$.

Because $\angle\;3$ and $\angle\;4$ are vertical, they must be equal. Therefore $\angle\;2=60^o$.