Question

1. if m∠ynm = 45°, what are m∠ynz and m∠znm?

Explanation:

Step1: Set up an equation

Since \(m\angle YNM=m\angle YNZ + m\angle ZNM\), we have \((6x - 2)+(2x - 1)=45\).

Step2: Combine like - terms

Combining the \(x\) terms and the constant terms on the left - hand side gives \(6x+2x-2 - 1=45\), which simplifies to \(8x-3 = 45\).

Step3: Solve for \(x\)

Add 3 to both sides of the equation: \(8x-3 + 3=45 + 3\), so \(8x=48\). Then divide both sides by 8: \(x=\frac{48}{8}=6\).

Step4: Find \(m\angle YNZ\)

Substitute \(x = 6\) into the expression for \(m\angle YNZ\): \(m\angle YNZ=6x-2=6\times6 - 2=36 - 2=34^{\circ}\).

Step5: Find \(m\angle ZNM\)

Substitute \(x = 6\) into the expression for \(m\angle ZNM\): \(m\angle ZNM=2x-1=2\times6 - 1=12 - 1 = 11^{\circ}\).

Answer:

\(m\angle YNZ = 34^{\circ}\), \(m\angle ZNM=11^{\circ}\)