Question

1. if m∠ecd = 7x + 20 and m∠acb = 2x + 80 find each value.

x =
m∠ecd =
m∠dcb =

Explanation:

Step1: Use vertical - angle property

Since $\angle ECD$ and $\angle ACB$ are vertical angles, $m\angle ECD=m\angle ACB$. So, $7x + 20=2x+80$.

Step2: Solve for $x$

Subtract $2x$ from both sides: $7x-2x + 20=2x-2x + 80$, which simplifies to $5x+20 = 80$. Then subtract 20 from both sides: $5x+20 - 20=80 - 20$, getting $5x=60$. Divide both sides by 5: $x=\frac{60}{5}=12$.

Step3: Find $m\angle ECD$

Substitute $x = 12$ into the expression for $m\angle ECD$. $m\angle ECD=7x + 20=7\times12+20=84 + 20=104$.

Step4: Find $m\angle DCB$

$\angle ECD$ and $\angle DCB$ are supplementary (a linear - pair), so $m\angle DCB=180 - m\angle ECD$. $m\angle DCB=180 - 104 = 76$.

Answer:

$x = 12$
$m\angle ECD=104$
$m\angle DCB=76$