Question

if m∠efv = 50°, m∠vfg = (63x − 1)°, and m∠efg = (88x − 1)°, find m∠vfg.

Explanation:

Step1: Use angle addition postulate

We know that \( m\angle EFG = m\angle EFV + m\angle VFG \). Substituting the given values, we get \((88x - 1)^\circ = 50^\circ + (63x - 1)^\circ\).

Step2: Solve for \(x\)

Simplify the equation:
\[

$$\begin{align*} 88x - 1 &= 50 + 63x - 1\\ 88x - 63x &= 50 - 1 + 1\\ 25x &= 50\\ x &= \frac{50}{25}\\ x &= 2 \end{align*}$$

\]

Step3: Find \(m\angle VFG\)

Substitute \(x = 2\) into \(m\angle VFG = (63x - 1)^\circ\):
\[

$$\begin{align*} m\angle VFG &= 63(2) - 1\\ &= 126 - 1\\ &= 125^\circ \end{align*}$$

\]

Answer:

\(125^\circ\)