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 $(7x + 4)+(8x - 1)=74$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms on the left - hand side gives $7x+8x + 4-1=74$, which simplifies to $15x+3 = 74$.

Step3: Solve for $x$

Subtract 3 from both sides: $15x=74 - 3=71$. Then $x=\frac{71}{15}$.

Step4: Find $\angle ABC$

Substitute $x$ into the expression for $\angle ABC$. $\angle ABC=(8x - 1)^{\circ}$, so $\angle ABC = 8\times\frac{71}{15}-1=\frac{568}{15}-1=\frac{568 - 15}{15}=\frac{553}{15}\approx36.87^{\circ}$.

Step5: Find $\angle DBC$

Substitute $x$ into the expression for $\angle DBC$. $\angle DBC=(7x + 4)^{\circ}$, so $\angle DBC=7\times\frac{71}{15}+4=\frac{497}{15}+4=\frac{497+60}{15}=\frac{557}{15}\approx37.13^{\circ}$.

Answer:

$m\angle ABC=\frac{553}{15}\approx36.87^{\circ}$, $m\angle DBC=\frac{557}{15}\approx37.13^{\circ}$