Final answer:
The sum of opposite angles formed by two intersecting lines is always 180°, while the product of opposite angles is not defined in geometry. The sum of adjacent angles formed by two intersecting lines is always 180°, while the product of adjacent angles is not a defined concept.
Step-by-step explanation:
The theorem that represents the sum of opposite angles formed by two intersecting lines is 180°. When two lines intersect, they form a pair of opposite angles, also known as vertical angles. Vertical angles are congruent, meaning that they have the same measure. Since the sum of the measures of two congruent angles is 180°, the sum of opposite angles formed by intersecting lines is always 180°.
On the other hand, the product of opposite angles formed by two intersecting lines is not always 90°. In fact, it is not a defined concept in geometry. Therefore, option (b) is not true.
We can also state the theorem for the sum of adjacent angles formed by two intersecting lines. When two lines intersect, they form four angles, with each pair of adjacent angles adding up to 180°. This is because adjacent angles are supplementary, meaning that their measures add up to 180°. Option (c) represents this theorem correctly.
Similarly, the product of adjacent angles formed by two intersecting lines is not defined in geometry, so option (d) is not true.
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