Find the value of each of the equal angles.
A) \[{{210}^{o}}\]
B) \[{{110}^{o}}\]
C) \[{{540}^{o}}\]
D) \[{{105}^{o}}\]
Correct Answer: D
Solution :
The pentagon can be divided into 3 triangles by joining the vertex A to C and D (See the figure). Angle sum of 1 triangle \[={{180}^{o}}\] Angle sum of 3 triangles \[=3\times {{180}^{o}}={{540}^{o}}\] Sum of the four equal angles \[={{540}^{o}}-{{120}^{o}}={{420}^{o}}\] Each equal angle \[={{420}^{o}}-4={{105}^{o}}\]
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