Question

Im older and Im not the best at these type of problems The measures of two complementary angles are described by the expressions (14z+9)° and (20z+13)°. Find the measures of the angles.

Answer 1

Complementary angles are two angles whose sum is 90 degrees. Graphically,

So, we can write and solve for x the following equation:

`\begin{gathered} m\angle1=(14z+9)\degree \\ m\angle2=\mleft(20z+13\mright)\degree \\ m\angle1+m\angle2=90\text{\degree} \end{gathered}`

`\begin{gathered} \mleft(14z+9\mright)\text{\degree}+\mleft(20z+13\mright)\text{\degree}=90\text{\degree} \\ (14z)\text{\degree}+9\text{\degree}+(20z)\text{\degree}+13\degree=90\text{\degree} \\ \text{ Add similar terms} \\ (34z)\text{\degree}+22\degree=90\text{\degree} \\ \text{ Subtract 22\degree{}from both sides} \\ (34z)\text{\degree}+22\degree-22\text{\degree}=90\text{\degree}-22\text{\degree} \\ (34z)\text{\degree}=68\text{\degree} \\ \text{ Divide by 34\degree{}from both sides} \\ \frac{(34z)\text{\degree}}{34\text{\degree}}=\frac{68\text{\degree}}{34\text{\degree}} \\ z=2 \end{gathered}`

Now, we replace the value of z in the measures of each angle:

`\begin{gathered} m\angle1=(14z+9)\degree \\ m\angle1=(14\cdot2+9)\degree \\ m\angle1=(28+9)\degree \\ m\angle1=37\text{\degree} \end{gathered}`
`\begin{gathered} m\angle2=(20z+13)\text{\degree} \\ m\angle2=(20\cdot2+13)\text{\degree} \\ m\angle2=(40+13)\text{\degree} \\ m\angle2=53\text{\degree} \end{gathered}`

Therefore, the measures of the angles are 37° and 53°.