Isosceles triangle with one angle of 100. What would most likely be the other angles?

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17-07-2015
Mathematics

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Isosceles triangle with one angle of 100. What would most likely be the other angles?

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RedRicin RedRicin · Answer 1 · 2015-07-17T03:21:20+02:00

Isoceles triangles have one pair of congruent base angles opposite their congruent sides. Also, the angles in a triangle add up to 180°. Therefore, we can set up this equation:

100 + x + x = 180

(we know it's not the 100° angle that has a congruent match because that would cause the total angle measure to go above 180°)

100 + 2x = 180
Subtract 100 from each side.
2x = 80
Divide by 2.
x = 40°

Both of the other angles would be 40°.

AL2006 AL2006 · Answer 2 · 2015-07-17T03:29:59+02:00

There's no "most likely" about it.

==> Every isosceles triangle has two equal angles.
==> In this one, the 100-degrees angle is either one of the two equal angles,
or else it isn't.
==> If the 100 is one of the two equal angles, then the other one is also 100,
and the sum of the angles in this triangle ... even without the third one ...
is already more than 180 degrees.
==> So the 100 CAN'T be one of the equal angles. It must be the third angle.

-- Now there are 80 degrees left over to split between the other two angles,
which ARE equal.

-- The other two angles, which are not 100 degrees, MUST be 40 degrees each.

Not probably, not maybe, not could-be, and not "most likely". They must be.