Q.155. Geometry - Finding sum of angles.

Question 155.

Find the sum of the missing angle measures as shown in the following diagram.

Answer 155.

Refer to the following figure.

Missing three angles of the inner hexagon are written in terms of "d" from the given information.
Adding the angles of the hexagon and equatting to 720°
=> c + d = 180° ... ( 1 )

 Missing two angles of the lower small triangle are written in terms of "a" and "d".
Adding the angles of the triangle,
a + d = 133° ... ( 2 )

 For the upper small triangle, external angle = external angle of right top triangle
=> e + 47 = d + 40°
=> d - e = 7° ... ( 3 )

 Subtracting ( 3 ) from ( 1 ),
c + e = 173° ... ( 4 )
For the left top triangle, external angle c = a + b.
Plugging c = a + b in ( 4 ),
a + b + e = 173° ... ( 5 )

 Adding ( 1 ) and ( 5 ),
a + b + c + d + e
= 180 + 173°
= 353°.

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