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If angle X in triangle is XYZ is 45º, is triangle XYZ an isosceles tri

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If angle X in triangle is XYZ is 45º, is triangle XYZ an isosceles tri  [#permalink]

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New post 29 Aug 2018, 00:29
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If angle X in triangle is XYZ is 45º, is triangle XYZ an isosceles triangle?

(1) The sum of angle Y and angle Z is 135º.
(2) The side opposite angle X is equal in length to the side opposite angle Y.

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Re: If angle X in triangle is XYZ is 45º, is triangle XYZ an isosceles tri  [#permalink]

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New post 29 Aug 2018, 00:37
For a triangle to be isosceles, two angles should be equal in a triangle.

From statement 1:
Y+Z = 135.
Y can be either 90 and Z can be 45. This will be an isosceles triangle.
But, If Y or Z takes any other angle, Then XYZ is not isosceles.
Hence 1 is insufficient.

From statement 2:
Angle X = Angle Y.
Then X = Y = 45.
Z must be 90. Since sum of angles in a triangle is 180.
Hence XYZ is isosceles triangle.

2 is sufficient.

B is the answer.
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Re: If angle X in triangle is XYZ is 45º, is triangle XYZ an isosceles tri &nbs [#permalink] 29 Aug 2018, 00:37
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