Question

if m∠abd = 82°, what are m∠abc and m∠dbc? m∠abc = □°

Explanation:

Step1: Set up an equation

Since $\angle ABD=\angle ABC + \angle DBC$, we have $(2x - 6)+(4x - 9)=82$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $(2x+4x)+(-6 - 9)=82$, which simplifies to $6x-15 = 82$.

Step3: Solve for $x$

Add 15 to both sides of the equation: $6x=82 + 15$, so $6x=97$. Then $x=\frac{97}{6}$.

Step4: Find $m\angle ABC$

Substitute $x=\frac{97}{6}$ into the expression for $\angle ABC$: $m\angle ABC=2x - 6=2\times\frac{97}{6}-6=\frac{97}{3}-6=\frac{97 - 18}{3}=\frac{79}{3}\approx26.33$.

Answer:

$\frac{79}{3}$