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MathLinks Contest 1st
1
0151 geometry 1st edition Round 5 p1
0151 geometry 1st edition Round 5 p1
Source:
May 9, 2021
geometry
1st edition
Problem Statement
In a triangle
A
B
C
ABC
A
BC
,
∠
B
=
7
0
o
\angle B = 70^o
∠
B
=
7
0
o
,
∠
C
=
5
0
o
\angle C = 50^o
∠
C
=
5
0
o
. A point
M
M
M
is taken on the side
A
B
AB
A
B
such that
∠
M
C
B
=
4
0
o
\angle MCB = 40^o
∠
MCB
=
4
0
o
, and a point
N
N
N
is taken on the side
A
C
AC
A
C
such that
∠
N
B
C
=
5
0
o
\angle NBC = 50^o
∠
NBC
=
5
0
o
. Find
∠
N
M
C
\angle NMC
∠
NMC
.
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