I need help with geometry

Question

The triangle ABC is given. At the extension of the side AB over the vertex A, the point M is chosen so that | AM | = | AC |. At the extension of the side AB over the vertex B, the point N is chosen so that | BN | = | BC |. Angle CMN = 27 °, and angle CNM = 32 °. What are the interior angles of triangle ABC?

Answer 1

Hi,

First, try to draw the triangle base of given information

1) triangle MAC is isosceles ======> when CMN = 27⁰ must be angle ACM = 27⁰ and angle CAM = 180 - ( 27 + 27 ) = 126⁰ on the other hand angle CAB = 180 - 126 = 54

by doing that you found one angle of triangle ABC

2) triangle NBC is isosceles ======> when CNM= 32⁰ must be angle NCB = 32⁰ and angle CBN = 180 - ( 32 + 32 ) = 116⁰ on the other hand angle CBA = 180 - 116 = 64

by doing that you found another angle of triangle ABC

3) in triangle ABC ===>

A= 54 AND B = 64 so you can find angle C of triangle ABC = 180 - ( 54 + 64 ) =62

I hope it is useful,

Minoo

Answer 2

Angle BAC = 27° + 27° = 54°; Angle ABC = 32° + 32° = 64°; Angle ACB = 180° - (54° + 64°) = 62°.

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