If the measure of angle ECD is six less than five times the measure of angle BCE, and the measure of angle BCD = 162 degrees, find each measure

Question

Please help me with this, show steps, work, and answers. This is for school and it is very difficult and I don't understand.

Answer 1

m∠BCD = 162°

Assume ∠BCE and ∠ECD are adjacent angles and share the line segment EC

where C is the vertex in all three angles

(Angle Additive Postulate)

m∠ECD = 5(m∠BCE) - 6

m∠ECD + m∠BCE = 162°

substitute 5(m∠BCE) - 6 for m∠ECD

5(m∠BCE) - 6 + m∠BCE = 162°

combine like terms

6(m∠BCE) - 6 = 162

get 6(m∠BCE) by itself on one side of equal sign

6(m∠BCE) - 6 + 6 = 162 + 6

6(m∠BCE) = 162 + 6

6(m∠BCE) = 168

Get unknown alone on one side of the equal sign

6(m∠BCE) / 6 = 168 / 6

m∠BCE = 28°

Plug in this measurement for m∠BCE to solve for m∠ECD

m∠ECD = 5(m∠BCE) - 6

m∠ECD = 5(28) - 6

m∠ECD = 140 - 6

m∠ECD = 134

Now check

m∠ECD + m∠BCE = m∠BCD

we know

m∠BCD = 162

m∠ECD + m∠BCE = 162°

substitute in the measurements for each angle

m∠ECD = 134°

m∠BCE = 28°

134° + 28° = 162°