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In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...
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06 Feb 2019, 18:59
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In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...
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Updated on: 06 Feb 2019, 19:49
EgmatQuantExpert wrote: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the sum of all possible values of ∠P? A. 70 B. 80 C. 100 D. 130 E. 150 IMO E Now PQR is an isosceles triangle, < Q = 80 3 Cases 1) when <P = < R = 50 2) when <Q = <P = 80 3) when <Q = <R = 80, <P = 20 Sum = 150
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Originally posted by KanishkM on 06 Feb 2019, 19:13.
Last edited by KanishkM on 06 Feb 2019, 19:49, edited 1 time in total.



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Re: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...
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06 Feb 2019, 19:44
KanishkM wrote: EgmatQuantExpert wrote: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the sum of all possible values of ∠P? A. 70 B. 80 C. 100 D. 130 E. 150 IMO E Now PQR is an isosceles triangle, < Q = 80 3 Cases 1) when <P = < R = 50 2) when <Q = <P = 80 3) when <Q = <R = 160, <P = 20Sum = 150 Hey KanishkM, 3) when <Q = <R = 160, <P = 20 How is it possible? While Sum of angles of triangle is 180
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In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...
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06 Feb 2019, 19:46
NandishSS wrote: KanishkM wrote: IMO E
Now PQR is an isosceles triangle, < Q = 80
3 Cases 1) when <P = < R = 50 2) when <Q = <P = 80 3) when <Q = <R = 160, <P = 20
Sum = 150
Hey KanishkM, 3) when <Q = <R = 160, <P = 20 How is it possible? While Sum of angles of triangle is 180 hahahah NandishSSI think i did some big time typo , let me correct it now
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Re: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...
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07 Feb 2019, 11:13
This is an isosceles triangle, so two sides are equal and two angles must be of the same measure.
There are three cases:
1) angle Q is formed by two equal sides, so the other two angles (P and R) must be the same.
\(80 (angle Q) + angle P + angle R = 180\) (sum of all angles in a triangle)
\(angle P + angle R = 100\)
As mentioned before, angle P and angle R must be equal, hence P = 50 and R = 50.
2) angle Q is formed by the base and one of the sides, and the angle (let's say R) is formed by the base and the other side. It means, that Q=R, so \(P = 1808080 = 20\)
3) angle Q is formed by the base and one of the sides, and the angle (this time it's P) is formed by the base and the other side. It means, that Q=P, so P = 80
Sum of all possible values of angle \(P = 50 + 20 + 80 = 150\).
Answer E.



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Re: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...
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07 Feb 2019, 21:43
EgmatQuantExpert wrote: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the sum of all possible values of ∠P? A. 70 B. 80 C. 100 D. 130 E. 150 P can be equal to 80, if side PR is the same length as QR. P can be 20 if side PQ is the same as PR P can be 50 if side PQ and RQ are the same. total is 150



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Re: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...
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07 Feb 2019, 23:09




Re: In an isosceles triangle PQR, if ∠Q = 80 degrees, then what is the ...
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