Answer:
m∠BCE = 28° and m∠ECD = 134°
Step-by-step 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°
