The angle that is equal to two-seventh of its supplement is 40°.
Two angles A and B are supplementary to each other, if and only if m ∠A + m ∠B = 180°.
In the question, we are asked to find the angle that is two-seventh of its supplement.
We assume the angle to be x°.
The supplement of this angle will be valued as (180 - x)°.
Now, we are told that the required angle is two-seventh of its supplement, that is, x = (2/7)(180 - x), which makes an equation in the variable x.
We can solve this equation as follows:
x = (2/7)(180 - x),
or, 7x = 360 - 2x,
or, 7x + 2x = 360,
or, 9x = 360,
or, x = 40.
Thus, the angle that is equal to two-seventh of its supplement is 40°.
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