Question

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

Explanation:

Step1: Set up an equation

Let $m\angle BCE = x$. Then $m\angle ECD=5x - 6$. Since $\angle BCD=\angle BCE+\angle ECD$ and $m\angle BCD = 162^{\circ}$, we have the equation $x+(5x - 6)=162$.

Step2: Simplify the left - hand side

Combine like terms: $x + 5x-6=6x-6$. So the equation becomes $6x-6 = 162$.

Step3: Solve for $x$

Add 6 to both sides of the equation: $6x-6 + 6=162 + 6$, which gives $6x=168$. Then divide both sides by 6: $x=\frac{168}{6}=28$. So $m\angle BCE = 28^{\circ}$.

Step4: Find $m\angle ECD$

Substitute $x = 28$ into the expression for $m\angle ECD$. $m\angle ECD=5x-6=5\times28 - 6=140 - 6=134^{\circ}$.

Answer:

$m\angle BCE = 28^{\circ}$
$m\angle ECD = 134^{\circ}$