Question

A and _B are supplementary angles. If m_A = (4x - 16) and m B = (8x + 4), then find the measure of ZA.

Answer 1

A=48

Explanation

Two Angles are Supplementary when they add up to 180 degrees

Step 1

if A and B are supplementary angles, then

$A+B=180$

Let

A=4x-16

B=8x+4

Step 2

replace,

$\begin{gathered} A+B=180 \\ 4x-16+8x+4=180 \\ 12x-12=180 \end{gathered}$

Step 3

solve for x

$\begin{gathered} 12x-12=180 \\ 12x=180+12 \\ 12x=192 \\ x=\frac{192}{12} \\ x=16 \\ \end{gathered}$

Step 4

finally, replace the value of x= 16 to find A

$\begin{gathered} A=4x-16 \\ A=4(16)-16 \\ A=64-16 \\ A=48 \end{gathered}$