Question

ZA and B are supplementary angles. If m_A = (x – 16)° and m

ZB = (3x + 28)°, then find the measure of ZA.

Answer 1

The Solution.

Two angles that are supplementary sum up to 180 degrees, this means that:

`\angle A+\angle B=180^o`
`\begin{gathered} \text{Where }\angle A=x-16 \\ \angle B=3x+28 \end{gathered}`
`\begin{gathered} x-16+3x+28=180 \\ \text{Collecting like terms, we get} \\ x+3x-16+28=180 \end{gathered}`
`\begin{gathered} 4x+12=180 \\ 4x=180-12 \\ 4x=168 \\ \text{Dividing both sides by 4, we get} \\ x=(168)/(4)=42 \end{gathered}`

To find angle A, we shall substitute 42 for x in the expression that defines angle A.

`\begin{gathered} \angle A=x-16 \\ \angle A=42-16=26^o \end{gathered}`

Therefore, the correct answer is 26 degrees.