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M∠8=100° and m∠7=30° what is the measure of angle 9

User Igal
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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.

User Djsumdog
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