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=) (^{circ}) (mangle2=) (^{circ})

Explanation:

Step1: Identify angle - relationship

Since $\angle1$ and $\angle2$ are complementary (they form a right - angle), their sum is 90 degrees.
$m\angle1 + m\angle2=90$

Step2: Substitute angle measures

Substitute $m\angle1=(8x)^{\circ}$ and $m\angle2=(x - 9)^{\circ}$ into the equation.
$8x+(x - 9)=90$

Step3: Simplify the left - hand side

Combine like terms: $8x+x-9 = 9x-9$.
$9x-9 = 90$

Step4: Solve for x

Add 9 to both sides: $9x=90 + 9=99$. Then divide both sides by 9, $x=\frac{99}{9}=11$.

Step5: Find $m\angle1$

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

Step6: Find $m\angle2$

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

Answer:

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