Five interior angles of a 10-sided figure are each 185 degrees. If the remaining five interior angles are equal, then each of the five angles (in degrees) is equal to:
103
The key principle is the formula for the sum of the interior angles of any polygon with n sides:
Sum of interior angles = (n − 2) × 180°.
This comes from the fact that an n-sided polygon can be divided into (n − 2) triangles from a single vertex, and each triangle contributes 180°.
For a 10-sided figure (decagon), n = 10:
- Sum of all interior angles = (10 − 2) × 180° = 8 × 180° = 1440°.
- Five of the angles are each 185°, contributing 5 × 185° = 925°. (An interior angle above 180° means the decagon is non-convex/reflex at those vertices, which is allowed since the sum formula still holds.)
- The remaining five equal angles together account for 1440° − 925° = 515°.
- Each such angle = 515° ÷ 5 = 103°.
So the correct answer is 103. A common error is to forget that the total must be 1440° and instead guess values near 105° or 107°; only 103° makes the five equal angles sum exactly to the leftover 515°.
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Important Questions from Geometry
If the angles of a triangle are in the ratio of 2:3:4, then the difference of the measure of greatest angle and smallest angle is
In ΔABC, ∠A = 90°, AD ┴ BC and AD = BD = 2 cm. The length of CD is
How many lines of symmetry does a rectangle have?
The number of diagonals in each face a cube is
Which of the following is/are the geometric figures with the line of symmetry?
I. Rectangle
II. Isosceles triangle
