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State True/False.

The bisectors of two adjacent supplementary angles include a right angle.

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True

False

answer is A.

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Detailed Solution

Considering the given figure:
Question Image

The supplementary angles are the two angles that add up to be

180 °

∠ A O C + ∠ B O C = 180 °

-------------------(1)
Let OC is the bisector of two adjacent supplementary angles, then,

∠ A O C = ∠ B O C

Put the value of

∠ A O C

in equation (1),

∠ B O C + ∠ B O C = 180 ° 2 ∠ B O C = 180 ° ∠ B O C = 90 °

Therefore, the bisectors between two given adjacent supplementary angles contain a right-angle.
Thus, the given statement is true.
Hence, option (1) is correct.

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