1)) three angles in the parallelogram? Submit

In a **parallelogram**, the properties of its angles are fundamental to understanding its geometry. A parallelogram has **four angles**, but they exhibit specific relationships: 1. **Opposite Angles are Equal**: - If we label the corners of the parallelogram as **A**, **B**, **C**, and **D** in sequence, then: - **∠A = ∠C** - **∠B = ∠D** 2. **Consecutive (Adjacent) Angles are Supplementary**: - This means that any two adjacent angles add up to **180 degrees**. - **∠A + ∠B = 180°** - **∠B + ∠C = 180°** - **∠C + ∠D = 180°** - **∠D + ∠A = 180°** 3. **Sum of All Interior Angles**: - The total of all four angles in a parallelogram is **360 degrees**. ### Example: Suppose you know one angle of a parallelogram is **70 degrees**. - **Opposite Angle**: The angle directly across from it is also **70 degrees**. - **Adjacent Angles**: Each adjacent angle will be **180° - 70° = 110 degrees**. So, the four angles of the parallelogram would be: - **70°, 110°, 70°, 110°** ### Visual Representation: ``` A _________ B | | | | D ‾‾‾‾‾‾‾‾ C ``` - **∠A = ∠C** - **∠B = ∠D** - **∠A + ∠B = 180°** ### Key Takeaways: - **Two distinct angle measures** in a parallelogram. - **Opposite angles** are **equal**. - **Adjacent angles** are **supplementary** (sum to 180°). Understanding these properties helps in solving various geometric problems related to parallelograms, such as finding unknown angles, proving congruency, and more. If you have a specific parallelogram with given angles or additional information, feel free to provide those details for a more tailored explanation!