Question

1. if m∠abc is one degree less than three times m∠abd and m∠dbc = 47°, find each measure.

m∠abd =

Explanation:

Step1: Set up equation

Let $m\angle ABD = x$. Then $m\angle ABC=3x - 1$ (since $m\angle ABC$ is one - degree less than three times $m\angle ABD$). Also, we know that $\angle ABC=\angle ABD+\angle DBC$, and $m\angle DBC = 47^{\circ}$. So, $3x - 1=x + 47$.

Step2: Solve the equation

Subtract $x$ from both sides: $3x-x-1=x - x+47$, which simplifies to $2x-1 = 47$. Then add 1 to both sides: $2x-1 + 1=47 + 1$, getting $2x=48$. Divide both sides by 2: $x=\frac{48}{2}=24$.

Answer:

$m\angle ABD = 24^{\circ}$