Answer in Brief
The supplement of an acute angle is .................
The supplement of an acute angle is an obtuse angle.
As the sum of the supplementary angles is 180°.
Let one of the angle measures x°, such that x < 90
Let the other angle measures y°
As the angles are supplementary there sum is 180°.
x + y = 180° ..... (1)
x < 90° ....... (2)
Now subracting (1) from (2)
-y < - 90°
y > 90°
Then, other angle y is clearly an obtuse angle.
Let the given acute angle be 30°
Then, the other angle becomes
(180 - 30)° = 150°
This is clearly an obtuse angle.
Concept: Introduction to Lines and Angles
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