Question

What is the value of x in degrees?

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​x​ =
°

Answer 1

all triangles add up to 180

Answer 2

180 degree*

Answer 3

angle Q is same as m<M( both triangles are the same )

Answer 4

Observe that, \[M(-1,6), L(-2,3), N(1,3).\]
Also, we have, \[Q(3,-4), P(2,-1), R(5,-1).\]
\[:. ML=\sqrt{(-1+2)^{2}+(6-3)^{2}}=\sqrt{10}.\]
\[LN=|-2-1|=3.\]
\[NM=\sqrt{(-1-1)^2+(6-3)^2}=\sqrt{13}.\]
Similarly, we can work out the distances,\[QP=\sqrt{10}, PR=3, RP=\sqrt{13}. \]
So, we have, \[ML=QP, LN=PR, NM=RQ.\]
Hence, triangle MLN is congruent to the triangle QPR (SSS).
\[:. <M=<Q=52^0, <L=<P=72^0, <N=<R=x^0.\]
But, in triangle MLN, \[<M +<L +<N=180^0.\]
\[:. 52^0+72^0+x^0=180^0.\]
\[:. x=180^0-52^0-72^0=56^0.\]