Question

hw 1.3.2 angle bisectors and perpendicular lines
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set up the equation and show all work on the test document
m∠abc =

Explanation:

Step1: Use angle - sum property

Since the two angles $9(x - 12)^{\circ}$ and $x^{\circ}$ are complementary (as the angle formed by the perpendicular lines is $90^{\circ}$), we set up the equation $9(x - 12)+x=90$.

Step2: Expand the left - hand side

Expand $9(x - 12)$ to get $9x-108$. So the equation becomes $9x-108 + x=90$.

Step3: Combine like terms

Combine the $x$ terms: $(9x + x)-108=90$, which simplifies to $10x-108 = 90$.

Step4: Isolate the variable term

Add 108 to both sides of the equation: $10x-108 + 108=90 + 108$, resulting in $10x=198$.

Step5: Solve for x

Divide both sides by 10: $x=\frac{198}{10}=19.8$.

Step6: Find the measure of $\angle ABC$

The measure of $\angle ABC$ is $x^{\circ}$, so $m\angle ABC = 19.8^{\circ}$.

Answer:

$19.8$