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In an isosceles triangle ABC, if the measure of angle A is 70°, which

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Bunuel
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In an isosceles triangle ABC, if the measure of angle A is 70°, which [#permalink] New post   27 Jun 2022, 04:15
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In an isosceles triangle ABC, if the measure of angle A is 70°, which of the following could be the measure of angle BCA?

I. 40°
II. 55°
III. 70°

(A) Only I
(B) Only III
(C) Only I and II
(D) Only II and III
(E) I, II and III
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Re: In an isosceles triangle ABC, if the measure of angle A is 70°, which [#permalink] New post   27 Jun 2022, 08:02
Don't fall into the trap in this question, that is, do not discount the fact that the other angle may not be 70 degrees.

If one angle is 70, then yes, the other MAY be 70, which means that III is possible, if the other angle is indeed 70, then the remaining (third) angle will be 180-70-70 = 40, so I is also possible.

But what if neither of the other angles are 70? Well if one angle is 70, and the other is 55, then the other must be 55 in an isosceles triangle.

55+55 = 110 + 70 =180, therefore, 55 is possible as well.

So I, II, and III could all be true
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Re: In an isosceles triangle ABC, if the measure of angle A is 70°, which [#permalink] New post   27 Jun 2022, 10:51
The possible measures of the other two angles are

70 and 40 or

55 and 55

Since you're free to choose which of the above is assigned to BCA, any one of the three works

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Re: In an isosceles triangle ABC, if the measure of angle A is 70°, which [#permalink] New post   27 Jun 2022, 12:07
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Isosceles triangle has two equal sides, so two equal angles.
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Re: In an isosceles triangle ABC, if the measure of angle A is 70°, which [#permalink]
27 Jun 2022, 12:07
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