Question

If m angle ECD is six less than five times m angle BCE, and mangle BCD = 162º. find each

measure.​

Answer 1

see explanation

Explanation:

let ∠BCE = x then ∠ECD = 5x - 6 and

∠BCE + ∠ECD = ∠BCD, substitute values

x + 5x - 6 = 162, that is

6x - 6 = 162 ( add 6 to both sides )

6x = 168 ( divide both sides by 6 )

x = 28

Hence

∠BCE = x = 28°

∠ECD = 5x - 6 = (5 × 28) - 6 = 140 - 6 = 134°

Answer 2

m∠BCE = 28º and m∠ECD=134º

Explanation:

Consider the provided figure.

From the figure it can observed that

m∠BCD= m∠ECD+ m∠BCE

It is given that m∠ECD is six less than five times m∠BCE, and m∠BCD = 162º.

Let the m∠BCE is xº then the m∠ECD can be written as:

m∠ECD=5x-6

Now substitute the value of m∠ECD and m∠BCE in above equation.

m∠BCD= 5x-6+ x

As we know m∠BCD = 162º

Thus,

162= 5x-6+ x

162+6= 6x

168= 6x

x=28

Thus, the m∠BCE = 28º

Now substitute the value of x in m∠ECD=5x-6

m∠ECD=5(28)-6

m∠ECD=140-6

m∠ECD=134º

Hence, the m∠BCE = 28º and m∠ECD=134º