Question

1. in the figure shown, m∠aed = 120. which of the following statements is false? not drawn to scale a. m∠aeb = 60 b. ∠bec and ∠ced are adjacent angles. c. m∠bec = 120 d. ∠aed and ∠bec are adjacent angles.

Explanation:

1. For option a: $\angle AED$ and $\angle AEB$ are supplementary (form a linear pair), so $m\angle AEB = 180 - 120 = 60$, so a is true.
2. For option b: $\angle BEC$ and $\angle CED$ share a common side ($EC$) and a common vertex ($E$), so they are adjacent angles, so b is true.
3. For option c: $\angle AED$ and $\angle BEC$ are vertical angles, so $m\angle BEC = m\angle AED = 120$, so c is true.
4. For option d: $\angle AED$ and $\angle BEC$ are vertical angles (opposite each other when two lines intersect), not adjacent (adjacent angles share a common side and vertex and don't overlap), so d is false.

Answer:

d. $\angle AED$ and $\angle BEC$ are adjacent angles.