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# In the figure shown below, what is the value of K ?

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Math Expert
Joined: 02 Sep 2009
Posts: 59730
In the figure shown below, what is the value of K ?  [#permalink]

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04 Oct 2018, 02:32
00:00

Difficulty:

25% (medium)

Question Stats:

87% (01:28) correct 13% (01:27) wrong based on 24 sessions

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In the figure shown below, what is the value of K?

(A) 45
(B) 50
(C) 55
(D) 65
(E) 70

Attachment:

2018-10-04_1331.png [ 32.23 KiB | Viewed 408 times ]

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Joined: 17 Mar 2018
Posts: 71
Re: In the figure shown below, what is the value of K ?  [#permalink]

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04 Oct 2018, 02:50
1
Right Triangle PSR is a 5-12-13. Hence, PR=13
Right Triangle PQT= 84^2 + pq^2= 85^2 --- PQ^2=85^2-84^2
PQ^2= (85+84)(85-84)= 169
PQ=13

Hence, Triangle PQR is an isosceles triangle
since, PQ= 13 and opposite angle Q= 65degrees, similarly PR=13, hence, opposite angle R= 65degrees
180-(2*65)= 50

Ans= B
Re: In the figure shown below, what is the value of K ?   [#permalink] 04 Oct 2018, 02:50
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