Question

1. if m∠ecd is six less than five times m∠bce, and m∠bcd = 162, find each measure. m∠bce = __ m∠ecd = __

Explanation:

Step1: Define variable for ∠BCE

Let \( m\angle BCE = x \).

Step2: Express ∠ECD in terms of x

\( m\angle ECD = 5x - 6 \).

Step3: Sum angles for ∠BCD

\( x + (5x - 6) = 162 \).

Step4: Solve for x

\( 6x - 6 = 162 \Rightarrow 6x = 168 \Rightarrow x = 28 \).

Step5: Find ∠ECD

\( m\angle ECD = 5(28) - 6 = 134 \).

Answer:

\( m\angle BCE = 28^\circ \)
\( m\angle ECD = 134^\circ \)