Choose the three true statements about the angles in the figure.

1. ∠1 and the 55° angle are adjacent.
2. m ∠1 = 55° because ∠1 and the 55° angle are vertical angles.
3. m ∠2 = 125° because ∠2 and the 55° angle are supplementary.
4. m ∠2 cannot be determined from the information given.
5. m ∠1 = 180° – 55°.
6. m ∠2 = 180° – 55° – 45°.

Question

Choose the three true statements about the angles in the figure.

1. ∠1 and the 55° angle are adjacent.
2. m ∠1 = 55° because ∠1 and the 55° angle are vertical angles.
3. m ∠2 = 125° because ∠2 and the 55° angle are supplementary.
4. m ∠2 cannot be determined from the information given.
5. m ∠1 = 180° – 55°.
6. m ∠2 = 180° – 55° – 45°.

Quizzma Team · Answer

To determine the true statements about the angles, let’s analyze each option:

1. True: ∠1 and the 55° angle are adjacent if they share a common side and vertex.
2. False: Vertical angles are equal; however, ∠1 cannot be equal to the 55° angle unless they are specifically vertical angles.
3. True: If ∠2 and the 55° angle are supplementary, then they add up to 180°. Thus, m ∠2 = 180° – 55° = 125°.
4. False: We can determine m ∠2 given the supplementary relationship with the 55° angle.
5. False: This statement implies that ∠1 is just the supplement of the 55° angle, which is not necessarily true unless it’s explicitly stated that ∠1 is supplementary to the 55° angle.
6. False: This is not a general rule without knowing the specific angles involved.

Thus, the three true statements are 1, 3, and 5.

Explanation:

– Statement 1 is true because adjacent angles share a side and vertex.

– Statement 3 is true through the supplementary relationship definition since ∠2 is described to be supplementary to the 55° angle.

– Statement 5 cannot be true based on valid angle relationships unless stated that ∠1 has

1 Answer