given: abcd is a parallelogram.
prove: ∠a and ∠d are supplementary.

by the definition of a parallelogram, ab∥dc. ad is a transversal between these sides, so ∠a and ∠d are ? angles. because ab and dc are ? , the same-side interior angles must be ? by the same-side interior angles theorem. therefore, ∠a and ∠d are supplementary.

Each person in an it department of 25 people works on at least one of 3 major projects: system security, program implementation, platform development. 10 people work on system security, 13 work on program implementation, and 12 work on platform development. 4 people work on system security and platform development, 5 people work on program implementation and platform development, and 2 people work on all three projects. how many people work on system security and program implementation?