Question

1. if m∠lmp is 11 degrees more than m∠wmp and m∠wml = 137°, find each measure.
2. if m∠abc is one degree less than three times m∠abd and m∠dbc = 47°, find each measure.

m∠abd =
m∠lmp =
m∠nmp =

Explanation:

Step1: Set up the equation for ∠ABC

We know that \(m\angle ABC=m\angle ABD + m\angle DBC\), and \(m\angle ABC = 3m\angle ABD- 1\), \(m\angle DBC = 47^{\circ}\). So \(3m\angle ABD-1=m\angle ABD + 47\).

Step2: Solve the equation for \(m\angle ABD\)

Subtract \(m\angle ABD\) from both sides: \(3m\angle ABD - m\angle ABD-1=m\angle ABD - m\angle ABD + 47\), which simplifies to \(2m\angle ABD-1 = 47\). Then add 1 to both sides: \(2m\angle ABD-1 + 1=47 + 1\), getting \(2m\angle ABD=48\). Divide both sides by 2: \(m\angle ABD=\frac{48}{2}=24^{\circ}\).

Answer:

\(m\angle ABD = 24^{\circ}\)