Question

1. if m∠ecd = 8x - 1 and m∠dcb = 7x - 14 find each value.

x =
m∠ecd =
m∠dcb =

Explanation:

Step1: Use linear - pair property

Since $\angle ECD$ and $\angle DCB$ form a linear - pair, $m\angle ECD + m\angle DCB=180^{\circ}$. So, $(8x - 1)+(7x - 14)=180$.

Step2: Simplify the left - hand side

Combine like terms: $8x+7x-1 - 14 = 180$, which gives $15x-15 = 180$.

Step3: Isolate the variable term

Add 15 to both sides of the equation: $15x-15 + 15=180 + 15$, resulting in $15x=195$.

Step4: Solve for x

Divide both sides by 15: $x=\frac{195}{15}=13$.

Step5: Find $m\angle ECD$

Substitute $x = 13$ into the expression for $m\angle ECD$: $m\angle ECD=8x - 1=8\times13-1=104 - 1 = 103^{\circ}$.

Step6: Find $m\angle DCB$

Substitute $x = 13$ into the expression for $m\angle DCB$: $m\angle DCB=7x - 14=7\times13-14=91 - 14 = 77^{\circ}$.

Answer:

$x = 13$
$m\angle ECD=103^{\circ}$
$m\angle DCB=77^{\circ}$