Question

Determine the measure of an angle whose measure is five times that of a supplement

Answer 1

In general, two angles are supplementary if their addition is equal to 180°; therefore, in our case, if x is the angle we need to find and y is its supplement,

`\begin{gathered} x+y=180 \\ \end{gathered}`

Furthermore, according to the problem,

`\begin{gathered} x=5y \\ \Rightarrow y=(x)/(5) \end{gathered}`

Solving for x,

`\begin{gathered} \Rightarrow x+(x)/(5)=180 \\ \Rightarrow(6x)/(5)=180 \\ \Rightarrow150 \end{gathered}`

Therefore, the answer to part a) is 150°

b) Two angles are complementary if their addition is equal to 90°, and the sum of the three interior angles of a triangle is 180°; thus, in our case, if z is the third angle,

`\begin{gathered} z+x+y=180 \\ \Rightarrow z+90=180 \\ \Rightarrow z=90 \end{gathered}`

The measure of the third angle is 90°