Dondo76idn
Answered

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Choose which statements are true:

I. Concave polygons have at least one interior angle more than 180°.
II. Regular polygons have equal sides and equal angles.
III. Convex polygons always have 5 sides.

A. I and III only
B. I and II only
C. I, II, and III
D. II only

Sagot :

GinnyAnsweridn
To determine which statements are true, let's examine each one individually:

Statement I: Concave polygons have at least one interior angle more than 180°.

- A concave polygon is defined as a polygon that has at least one interior angle greater than 180°. This causes the polygon to "cave inwards" at that angle.
- Since concave polygons must have an interior angle greater than 180°, this statement is true.

Statement II: Regular polygons have equal sides and equal angles.

- A regular polygon is a polygon that is both equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
- Therefore, by definition, regular polygons must have equal sides and equal angles, making this statement true.

Statement III: Convex polygons always have 5 sides.

- A convex polygon is a polygon where all interior angles are less than 180°, and no sides "cave inwards".
- However, convex polygons can have any number of sides greater than or equal to three. They are not restricted to having exactly 5 sides; a triangle, quadrilateral, hexagon, etc., can all be convex.
- Since not all convex polygons must have 5 sides, this statement is false.

Given these evaluations:
- Statement I is true.
- Statement II is true.
- Statement III is false.

The correct option that reflects which statements are true is B (I and II only).
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