Question

find the m∠dwn.

Explanation:

Step1: Apply angle - sum property of a triangle

In a triangle, the sum of interior angles is 180 degrees. So for \(\triangle DWN\), we have \(3x+(7x - 15)+5x=180\).

Step2: Combine like - terms

Combining the \(x\) terms, we get \((3x + 7x+5x)-15 = 180\), which simplifies to \(15x-15 = 180\).

Step3: Add 15 to both sides

\(15x-15 + 15=180 + 15\), so \(15x=195\).

Step4: Solve for \(x\)

Dividing both sides by 15, we have \(x=\frac{195}{15}=13\).

Step5: Find the measure of \(\angle DWN\)

Since \(\angle DWN = 3x\), substituting \(x = 13\), we get \(m\angle DWN=3\times13 = 39\) degrees.

Answer:

39 degrees