Question

3 numeric 1 point line ab is parallel to line de. what is the measure of ∠ecb in degrees? answer

Explanation:

Step1: Find the alternate - interior angle to $\angle BAC$

Since $AB\parallel DE$, $\angle BAC$ and the angle at $C$ (let's call it $\angle ACD$) which is an alternate - interior angle are equal. $\angle BAC = 180^{\circ}- 115^{\circ}=65^{\circ}$ (linear - pair of angles). So $\angle ACD = 65^{\circ}$.

Step2: Use the angle - sum property of a triangle

In $\triangle ABC$, we know one angle at $B = 35^{\circ}$ and we want to find $\angle ECB$.
We know that the sum of angles on a straight line is $180^{\circ}$. Also, in $\triangle ABC$, considering the angles around point $C$.
We know that $\angle ACD+\angle ECB + 35^{\circ}=180^{\circ}$ (angles on a straight line).
We already found $\angle ACD = 65^{\circ}$.
Substitute $\angle ACD$ into the equation: $65^{\circ}+\angle ECB+35^{\circ}=180^{\circ}$.
$\angle ECB=180^{\circ}-(65^{\circ} + 35^{\circ})$.
$\angle ECB = 80^{\circ}$.

Answer:

$80$