Final Answer:
The angles m∠1, m∠2, m∠3, m∠4, m∠5, m∠6, m∠7 all have a measure of 180° - x°.
Step-by-step explanation:
In geometry, when an angle m∠8 is given a measure x°, and it is mentioned that certain angles have a measure of 180° - x°, it implies a relationship between these angles and the supplementary property. The supplementary property states that when two angles add up to 180°, they are considered supplementary. In this case, the angles m∠1, m∠2, m∠3, m∠4, m∠5, m∠6, m∠7are all supplementary to m∠8, as their collective measures sum to 180°.
To visualize this, imagine m∠8 on a straight line. The mentioned angles are placed on the same line, and together they form a straight angle. By the supplementary property, the sum of their measures equals 180°. Therefore, each individual angle has a measure of 180° - x°. This understanding is essential in geometry to identify angle relationships within a given configuration.
In summary, recognizing the supplementary nature of angles arranged in a straight line allows us to conclude that the measures of m∠1, m∠2, m∠3, m∠4, m∠5, m∠6, m∠7 are indeed 180° - x°, providing a foundational insight into solving geometry problems involving angle measures.