Question

in the figure below, (mangle1=(x - 9)^{circ}) and (mangle2 = 8x^{circ}). find the angle measures.

Explanation:

Step1: Observe angle relationship

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

Step2: Combine like terms

Combine the $x$ terms on the left - hand side:
$x+8x-9 = 90$
$9x-9 = 90$

Step3: Add 9 to both sides

$9x-9 + 9=90 + 9$
$9x=99$

Step4: Solve for x

Divide both sides by 9:
$x=\frac{99}{9}=11$

Step5: Find $m\angle1$

Substitute $x = 11$ into the expression for $m\angle1$:
$m\angle1=(x - 9)^{\circ}=(11 - 9)^{\circ}=2^{\circ}$

Step6: Find $m\angle2$

Substitute $x = 11$ into the expression for $m\angle2$:
$m\angle2=8x^{\circ}=8\times11^{\circ}=88^{\circ}$

Answer:

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