Final Answer:
The measure of angle 9 is 50°, calculated by subtracting the sum of angles 8 and 7 from 180° as they form a straight line.
Step-by-step explanation:
Angles 8 (∠8) and 7 (∠7) are adjacent angles that form a straight line. According to the linear pair postulate, when two angles are adjacent and form a straight line, their measures sum up to 180°. Therefore, the measure of angle 8 (∠8) is 100°, and the measure of angle 7 (∠7) is 30°. Given that angles 8 and 7 are adjacent and supplementary, we can find the measure of angle 9 (∠ by9) subtracting the sum of angles 8 and 7 from 180°:
Angle 8 (∠8) + Angle 7 (∠7) + Angle 9 (∠9) = 180°
Substituting the given angle measures:
100° + 30° + Angle 9 (∠9) = 180°
To find the measure of angle 9:
Angle 9 (∠9) = 180° - (100° + 30°)
Angle 9 (∠9) = 180° - 130°
Angle 9 (∠9) = 50°
Therefore, the measure of angle 9 (∠9) is 50°. This calculation applies the supplementary property of adjacent angles forming a straight line to determine the unknown angle measure. Understanding angle relationships and applying geometric principles aids in solving for unknown angles in various geometric configurations.