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In an isosceles triangle PQR, if the measure of angle P is 80°, which

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In an isosceles triangle PQR, if the measure of angle P is 80°, which  [#permalink]

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New post 04 Oct 2018, 01:37
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In an isosceles triangle PQR, if the measure of angle P is 80°, which of the following could be the measure of angle R ?

I. 20°
II. 50°
III. 80°

(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 PQR, if the measure of angle P is 80°, which  [#permalink]

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New post 04 Oct 2018, 02:07
E
If angle Q= 80, then R=20
If angle Q= 20, then R= 80
If angle P is the largest angle, then Angle Q and angle R= 50 .
So all 3 choices are possible for Angle R.
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Re: In an isosceles triangle PQR, if the measure of angle P is 80°, which  [#permalink]

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New post 04 Oct 2018, 07:52
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Bunuel wrote:
In an isosceles triangle PQR, if the measure of angle P is 80°, which of the following could be the measure of angle R ?

I. 20°
II. 50°
III. 80°

(A) Only I
(B) Only III
(C) Only I and II
(D) Only II and III
(E) I, II and III


An isosceles triangle has two equal angles .
So, there are two possible cases here:

case i) 80° is one of the duplicate angles, in which case there are two angles measuring 80° and the other angle is 20°
So, I and III are possible

case ii) 80° is NOT one of the duplicate angles, in which case one angle is 80° and the other two (duplicate) angles are each 50°
So, II is possible

Answer: E

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Re: In an isosceles triangle PQR, if the measure of angle P is 80°, which  [#permalink]

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New post 07 Oct 2018, 18:25
Bunuel wrote:
In an isosceles triangle PQR, if the measure of angle P is 80°, which of the following could be the measure of angle R ?

I. 20°
II. 50°
III. 80°

(A) Only I
(B) Only III
(C) Only I and II
(D) Only II and III
(E) I, II and III


Since triangle PQR is isosceles, angles P and R could be 80 degrees, and angle Q could be 20 degrees.

On the other hand, if angles Q and P were each 80 degrees, then angle R would be 180 - 2(80) = 20.

Furthermore, angle P could be the vertex angle of 80 degrees, and angle R could be one of the base angles. If that were the case, then angle R would be (180 - 80)/2 = 50.

Answer: E
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Re: In an isosceles triangle PQR, if the measure of angle P is 80°, which &nbs [#permalink] 07 Oct 2018, 18:25
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