Question

in the figure, (mangle1=(x - 18)^{circ}) and (mangle2=(8x)^{circ}). (a) write an equation to find (x). make sure you use an \=\ sign in your answer. equation: (b) find the degree measure of each angle. (mangle1=) (^{circ}) (mangle2=) (^{circ})

Explanation:

Step1: Identify angle - relationship

Since $\angle1$ and $\angle2$ are supplementary (a straight - line angle is 180°), we set up the equation.
$(x - 18)+8x=180$

Step2: Combine like terms

Combine the $x$ terms on the left - hand side of the equation.
$x+8x-18 = 180$
$9x-18=180$

Step3: Isolate the variable term

Add 18 to both sides of the equation.
$9x-18 + 18=180 + 18$
$9x=198$

Step4: Solve for x

Divide both sides of the equation by 9.
$x=\frac{198}{9}=22$

Step5: Find the measure of $\angle1$

Substitute $x = 22$ into the expression for $m\angle1$.
$m\angle1=(x - 18)^{\circ}=(22-18)^{\circ}=4^{\circ}$

Step6: Find the measure of $\angle2$

Substitute $x = 22$ into the expression for $m\angle2$.
$m\angle2=(8x)^{\circ}=(8\times22)^{\circ}=176^{\circ}$

Answer:

(a) Equation: $(x - 18)+8x=180$
(b) $m\angle1 = 4^{\circ}$
$m\angle2 = 176^{\circ}$