Question

drag and drop your answers into the boxes to complete the explanation.
$\angle aeb$, $\angle 3$, $\angle dec$ form a \boxed{\quad}, so \boxed{\quad}. therefore, $m\angle 3 = \boxed{\quad}$.
$m\angle 1 = \boxed{\quad}$ because $\angle aeb$ and $\angle 1$ are \boxed{\quad}. $m\angle 2 = \boxed{\quad}$ because $\angle dec$ and $\angle 2$ are also \boxed{\quad}. since $45 + 70 + 65 = 180$, by

Explanation:

Step1: Identify angle relationship

$\angle AEB$, $\angle 3$, $\angle DEC$ lie on a straight line, so they form a straight angle (sum to $180^\circ$).

Step2: Calculate $m\angle3$

Use straight angle sum:
$$m\angle3 = 180^\circ - m\angle AEB - m\angle DEC$$
$$m\angle3 = 180^\circ - 45^\circ - 65^\circ = 70^\circ$$

Step3: Find $m\angle1$

$\angle AEB$ and $\angle1$ are alternate interior angles (since $BC \parallel AD$), so $m\angle1 = m\angle AEB = 45^\circ$.

Step4: Find $m\angle2$

$\angle DEC$ and $\angle2$ are alternate interior angles (since $BC \parallel AD$), so $m\angle2 = m\angle DEC = 65^\circ$.

Step5: Verify angle sum rule

The sum $45^\circ + 70^\circ + 65^\circ = 180^\circ$ confirms the triangle angle sum theorem for $\triangle BEC$.

Answer:

$\angle AEB, \angle3, \angle DEC$ form a $\boldsymbol{\text{straight angle}}$, so $\boldsymbol{m\angle AEB + m\angle3 + m\angle DEC = 180^\circ}$. Therefore, $m\angle3 = \boldsymbol{70^\circ}$
$m\angle1 = \boldsymbol{45^\circ}$ because $\angle AEB$ and $\angle1$ are $\boldsymbol{\text{alternate interior angles}}$
$m\angle2 = \boldsymbol{65^\circ}$ because $\angle DEC$ and $\angle2$ are also $\boldsymbol{\text{alternate interior angles}}$. Since $45 + 70 + 65 = 180$, by $\boldsymbol{\text{triangle angle sum theorem}}$