Question

problem 16: (first taught in lesson 12) if \\(\overrightarrow{ce}\\) bisects \\(\angle dcf\\), and if \\(m\angle dce = x - 11\\) and \\(m\angle ecf = 166 - 2x\\), then find \\(m\angle ecf\\). after you enter your answer press go. \\(m\angle ecf = \square\\)

Explanation:

Step1: Use angle bisector property

Since \( \overrightarrow{CE} \) bisects \( \angle DCF \), \( m\angle DCE = m\angle ECF \). So we set up the equation: \( x - 11 = 166 - 2x \).

Step2: Solve for \( x \)

Add \( 2x \) to both sides: \( x + 2x - 11 = 166 \), which simplifies to \( 3x - 11 = 166 \). Then add 11 to both sides: \( 3x = 166 + 11 = 177 \). Divide both sides by 3: \( x = \frac{177}{3} = 59 \).

Step3: Find \( m\angle ECF \)

Substitute \( x = 59 \) into \( m\angle ECF = 166 - 2x \): \( 166 - 2\times59 = 166 - 118 = 48 \).

Answer:

48