Question

In the adjoining figure, AB//CD. Given that AEC = 62° and BEF = 78°, find the values of ECF, EFC, and ZEFD.

Answer 1

1.
`\angle ECF` = 116°

2.
`\( \angle EFC`= 62°

3.
`\( \angle ZEFD` = 78°

Step-by-step explanation:

In the given figure,
`\( AB \)` is parallel to CD , and we are provided with the angles AEC = 62° and BEF = 78° .

Firstly, we can find
`\( \angle ECF \)` by recognizing that AEC and ECF are corresponding angles as
`\( AB \parallel CD \)`. Therefore,
`\( \angle ECF` =
`\angle AEC = 62° \).`

Next,
`\( \angle EFC \)`can be determined as the interior angle of the triangle
`\( BEF \)`. Since the sum of angles in a triangle is 180° ,
`\( \angle EFC` = 180° -
`\angle BEF - \angle BEC` = 180° - 78° - 40° = 62° \).

Finally,
`\( \angle ZEFD \)` is the vertical angle to
`\( \angle BEF \)`. Vertical angles are always congruent, so
`\( \angle ZEFD = \angle BEF` = 78° .

In summary,
`\( \angle ECF` = 62° ,
`\( \angle EFC`= 62° , and
`\( \angle ZEFD` = 78° are the final values for the given angles in the figure. The solution is derived through the application of angle properties in parallel lines and triangles, ensuring a comprehensive understanding of geometric principles.