Question

if m∠abd = 74°, what are m∠abc and m∠dbc? m∠abc = □°

Explanation:

Step1: Set up an equation

Since $\angle ABD=\angle ABC+\angle DBC$, we have $(8x - 3)+(7x - 4)=74$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms on the left - hand side gives $8x+7x-3 - 4 = 74$, which simplifies to $15x-7 = 74$.

Step3: Solve for $x$

Add 7 to both sides of the equation: $15x-7 + 7=74 + 7$, so $15x=81$. Then divide both sides by 15: $x=\frac{81}{15}=\frac{27}{5}=5.4$.

Step4: Find $\angle ABC$

Substitute $x = 5.4$ into the expression for $\angle ABC$: $m\angle ABC=8x-3=8\times5.4-3=43.2 - 3=40.2^{\circ}$.

Step5: Find $\angle DBC$

Substitute $x = 5.4$ into the expression for $\angle DBC$: $m\angle DBC=7x-4=7\times5.4-4=37.8 - 4=33.8^{\circ}$.

Answer:

$m\angle ABC = 40.2^{\circ}$, $m\angle DBC = 33.8^{\circ}$