Question

in the figure below, (mangle1=(x - 18)^{circ}) and (mangle2 = 8x^{circ}). find the angle measures.

Explanation:

Step1: Assume angles are supplementary

Since $\angle1$ and $\angle2$ form a straight - line, $m\angle1 + m\angle2=180^{\circ}$. So, $(x - 18)+8x=180$.

Step2: Combine like terms

$x+8x-18 = 180$, which simplifies to $9x-18 = 180$.

Step3: Solve for $x$

Add 18 to both sides: $9x=198$. Then divide by 9, $x = 22$.

Step4: Find angle measures

$m\angle1=(x - 18)^{\circ}=(22 - 18)^{\circ}=4^{\circ}$. $m\angle2=8x^{\circ}=8\times22^{\circ}=176^{\circ}$.

Answer:

$m\angle1 = 4^{\circ}$
$m\angle2 = 176^{\circ}$