Question

if m∠abd = 83° and m∠abc=(x + 10)° and m∠dbc=(4x - 12)°, what is the measure of each angle? enter the correct numbers in the boxes. m∠abc = m∠dbc =

Explanation:

Step1: Set up equation based on angle - addition

Since $\angle ABD=\angle ABC+\angle DBC$, we have the equation $(x + 10)+(4x-12)=83$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms: $(x + 4x)+(10 - 12)=83$, which simplifies to $5x-2 = 83$.

Step3: Isolate the variable term

Add 2 to both sides of the equation: $5x-2 + 2=83 + 2$, resulting in $5x=85$.

Step4: Solve for $x$

Divide both sides by 5: $\frac{5x}{5}=\frac{85}{5}$, so $x = 17$.

Step5: Find $\angle ABC$

Substitute $x = 17$ into the expression for $\angle ABC$: $\angle ABC=(x + 10)^{\circ}=(17 + 10)^{\circ}=27^{\circ}$.

Step6: Find $\angle DBC$

Substitute $x = 17$ into the expression for $\angle DBC$: $\angle DBC=(4x-12)^{\circ}=(4\times17-12)^{\circ}=(68 - 12)^{\circ}=56^{\circ}$.

Answer:

$m\angle ABC = 27$
$m\angle DBC = 56$