Question

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

Explanation:

Step1: Set up equation

Let $m\angle ABD = x$. Then $m\angle ABC=3x - 1$. Since $\angle ABC=\angle ABD+\angle DBC$ and $\angle DBC = 47^{\circ}$, we have $3x - 1=x + 47$.

Step2: Solve for x

Subtract x from both sides: $3x - x-1=x - x + 47$, which gives $2x-1 = 47$. Add 1 to both sides: $2x=48$. Divide by 2: $x = 24$.

Step3: Find angle measures

$m\angle ABD=x = 24^{\circ}$. $m\angle ABC=3x - 1=3\times24 - 1=71^{\circ}$.

Answer:

$m\angle ABD = 24^{\circ}$, $m\angle ABC=71^{\circ}$