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------------------------------------------------ 1) Using the map above, if angle 1 is 54 degrees and angle 3 is 82 degrees find the measures of the rest of the angles listed here. (Hint: some may not be able to be found) Angle 2 = 116 Angle 4 = 116 Angle 5 = 116 Angle 6 = 64 Angle 7 = 116 Angle 8 = 64 Angle 9 = 116 Angle 10 = 64

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Answer :

The measures of the rest of the angles listed here are:

Angle 2 = 126 degrees

Angle 4 = 126 degrees

Angle 5 = 126 degrees

Angle 6 = 54 degrees

Angle 7 = 82 degrees

Angle 8 = 54 degrees

Angle 9 = 82 degrees

Angle 10 = 54 degrees

Angle 2 = 116

Angle 2 is supplementary to angle 1, so 2 + 1 = 180. Therefore, angle 2 = 180 - 54 = 126 degrees.

Angle 4 = 116

Angle 4 is alternate interior angles to angle 2, which is 126 degrees. Alternate interior angles are always equal, so angle 4 = 126 degrees.

Angle 5 = 116

Angle 5 is corresponding angles to angle 2, which is 126 degrees. Corresponding angles are always equal, so angle 5 = 126 degrees.

Angle 6 = 64

Angle 6 is vertical angles to angle 1, which is 54 degrees. Vertical angles are always equal, so angle 6 = 54 degrees.

Angle 7 = 116

Angle 7 is corresponding angles to angle 3, which is 82 degrees. Corresponding angles are always equal, so angle 7 = 82 degrees.

Angle 8 = 64

Angle 8 is alternate interior angles to angle 6, which is 54 degrees. Alternate interior angles are always equal, so angle 8 = 54 degrees.

Angle 9 = 116

Angle 9 is corresponding angles to angle 7, which is 82 degrees. Corresponding angles are always equal, so angle 9 = 82 degrees.

Angle 10 = 64

Angle 10 is alternate interior angles to angle 8, which is 54 degrees. Alternate interior angles are always equal, so angle 10 = 54 degrees.

Therefore, the measures of the rest of the angles listed here are:

Angle 2 = 126 degrees

Angle 4 = 126 degrees

Angle 5 = 126 degrees

Angle 6 = 54 degrees

Angle 7 = 82 detgrees

Angle 8 = 54 degrees

Angle 9 = 82 degrees

Angle 10 = 54 degrees

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