1. Identify the given angles: ∠ADE = 76° and ∠BEF = 39°.
2. Recognize that lines CF and GJ are parallel, and lines AD and BL are transversals intersecting them.
3. Use the property of alternate interior angles: Since CF || GJ, the alternate interior angle to ∠ADE (which is 76°) at point H on line GJ is also 76°. This angle is ∠DHG.
4. Similarly, the alternate interior angle to ∠BEF (which is 39°) at point H on line GJ is also 39°. This angle is ∠EHG.
5. Observe that ∠DHG and ∠EHG are adjacent angles that together form the straight angle ∠DHE along line GJ.
6. The angle x° is the vertical angle to ∠DHE.
7. Calculate ∠DHE: Since ∠DHG and ∠EHG are adjacent and lie on a straight line, their sum is 180°. Therefore, ∠DHE = 180° - (∠DHG + ∠EHG) = 180° - (76° + 39°) = 180° - 115° = 65°.
8. Since vertical angles are equal, x° = ∠DHE = 65°.
Parent Tip: Review the logic above to help your child master the concept of alternate angles worksheet.
