Question

If m<ECD is six less than five times m<BCE. and m<BCD = 162°, find each measure.(Sorry bout using the wrong signs, but < is meant to represent angle)​

Answer 1

m∠BCE = 28°

m∠ECD = 134°

Explanation:

Statement in the question says " m∠ECD is six less than five times m∠BCE.

m∠ECD = 5(m∠BCE) - 6

m∠BCD = 162°

SInce m∠BCD = m∠BCE + m∠ECD

162° = m∠BCE + 5(m∠BCE) - 6

162° = 6(m∠BCE) - 6

162 + 6 = 6(m∠BCE)

168 = 6(m∠BCE)

m∠BCE =
`(168)/(6)`

m∠BCE = 28°

Since m∠BCD = m∠BCE + m∠ECD

162 = 28 + m∠ECD

m∠ECD = 162 - 28 = 134°

Therefore, m∠BCE = 28° and m∠ECD = 134° is the answer.

Answer 2

m∠BCE = 28° and m∠ECD = 134°

Explanation:

* Lets explain how to solve the problem

- The figure has three angles: ∠BCE , ∠ECD , and ∠BCD

- m∠ECD is six less than five times m∠BCE

- That means when we multiply measure of angle BCE by five and

then subtract six from this product the answer will be the measure

of angle ECD

∴ m∠ECD = 5 m∠BCE - 6 ⇒ (1)

∵ m∠BCD = m∠BCE + m∠ECD

∵ m∠BCD = 162°

∴ m∠BCE + m∠ECD = 162 ⇒ (2)

- Substitute equation (1) in equation (2) to replace angle ECD by

angle BCE

∴ m∠BCE + (5 m∠BCE - 6) = 162

- Add the like terms

∴ 6 m∠BCE - 6 = 162

- Add 6 to both sides

∴ 6 m∠BCE = 168

- Divide both sides by 6

∴ m∠BCE = 28°

- Substitute the measure of angle BCE in equation (1) to find the

measure of angle ECD

∵ m∠ECD = 5 m∠BCE - 6

∵ m∠BCE = 28°

∴ m∠ECD = 5(28) - 6 = 140 - 6 = 134°

* m∠BCE = 28° and m∠ECD = 134°