Question

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

Explanation:

Step1: Set up equations

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

Step2: Solve the equation for x

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

Step3: Find $m\angle ABC$

Substitute $x = 24$ into the expression for $m\angle ABC$. $m\angle ABC=3x - 1=3\times24-1=72 - 1=71^{\circ}$.

Answer:

$71^{\circ}$