Question

in the figure, m∠1=(8x)° and m∠2=(x - 9)°. (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. m∠1=° m∠2=°

Explanation:

Step1: Identify angle relationship

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

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 $m\angle1$:
$m\angle1=8x=8\times11 = 88^{\circ}$

Step4: Find the measure of $\angle2$

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) $m\angle1 = 88^{\circ}$
$m\angle2 = 2^{\circ}$