Question

in the figure, (mangle1=(8x)^{circ}) and (mangle2=(x - 9)^{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=) (mangle2=)

Explanation:

Step1: Identify angle - relationship

Since $\angle1$ and $\angle2$ are complementary (as they form a right - angle), we have $m\angle1 + m\angle2=90^{\circ}$.
$(8x)+(x - 9)=90$

Step2: Solve the equation for $x$

Combine like terms: $8x+x-9 = 90$.
$9x-9=90$.
Add 9 to both sides: $9x=90 + 9$.
$9x=99$.
Divide both sides by 9: $x=\frac{99}{9}=11$.

Step3: Find the measure of $\angle1$

Substitute $x = 11$ into the expression for $m\angle1$: $m\angle1=8x$.
$m\angle1=8\times11 = 88^{\circ}$.

Step4: Find the measure of $\angle2$

Substitute $x = 11$ into the expression for $m\angle2$: $m\angle2=x - 9$.
$m\angle2=11-9 = 2^{\circ}$.

Answer:

(a) Equation: $8x+(x - 9)=90$
(b) $m\angle1 = 88^{\circ}$
$m\angle2 = 2^{\circ}$