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Sagot :
Two angles are supplementary if the sum of their measures is equal to 180°. In part A we are told that an angle measures 42° and we have to find its supplement. Using what I stated before, the measure of the supplement (x) plus 42° must be equal to 180°:
[tex]180^{\circ}=42^{\circ}+x[/tex]We can substract 42° from both sides:
[tex]\begin{gathered} 180^{\circ}-42^{\circ}=42^{\circ}+x-42^{\circ} \\ 138^{\circ}=x \end{gathered}[/tex]So the answer to part A is 138°.
Two angles are complementary if the sum of their measures is equal to 90°. In part B we have to find the measure of the complement (y) of 61°. Following the definition of complementary angles the sum of y and 61° is equal to 90° then:
[tex]y+61^{\circ}=90^{\circ}[/tex]We can substract 61° from both sides:
[tex]\begin{gathered} y+61^{\circ}-61^{\circ}=90^{\circ}-61^{\circ} \\ y=29^{\circ} \end{gathered}[/tex]Then the answer to part B is 29°.
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