A regular 5-sided polygon has been divided into 5 congruent triangles by lines drawn from the center of the polygon to its vertices. What is the value of angle m?
A) 80 degrees
B) 54 degrees
C) 74 degrees
D) 40 degrees
E) 60 degrees
Answer: B
Since it is a regular polygon, all sides are equal. Furthermore, if all the lines are drawn from the center, their lengths must be the same, and the triangles are isosceles.
The sum of all the angles around the center point is 360°.
Since there are 5 triangles, each central angle is
360 ÷ 5 = 72°.
The sum of the angles in each triangle is 180°.
180 – 72 = 108°.
Each base angle is
108 ÷ 2 = 54°.
Therefore, m = 54°
✅ Answer: B (54 degrees)
💡 Know your fundamentals — regular polygons often hide simple math tricks like this one!
A) 80 degrees
B) 54 degrees
C) 74 degrees
D) 40 degrees
E) 60 degrees
Answer: B
Since it is a regular polygon, all sides are equal. Furthermore, if all the lines are drawn from the center, their lengths must be the same, and the triangles are isosceles.
The sum of all the angles around the center point is 360°.
Since there are 5 triangles, each central angle is
360 ÷ 5 = 72°.
The sum of the angles in each triangle is 180°.
180 – 72 = 108°.
Each base angle is
108 ÷ 2 = 54°.
Therefore, m = 54°
✅ Answer: B (54 degrees)
💡 Know your fundamentals — regular polygons often hide simple math tricks like this one!
