Quadrilateral Identification: Analyzing a Four-Sided Figure with Marked Angles

Indicate the correct answer

The next quadrilateral is:

Initially, let us examine the basic properties of a deltoid (or kite):

A quadrilateral is classified as a deltoid if:

• It has two distinct pairs of adjacent sides that are equal in length.

In the question's image, we observe the following:

• There are lines connecting A to B, B to C, C to D, and D to A, suggesting a typical quadrilateral.
• The shape, given its central symmetry (as it is formed by joining these particular points which extend equal lines), is reminiscent of a symmetric or bilaterally mirrored formation.
• Given the symmetry, it suggests all internal angles are less than 180 degrees, confirming the figure as a convex shape.

From this analysis, the quadrilateral satisfies the characteristic of having pairs of equal adjacent sides which confirms it as a deltoid. The symmetry suggests it is not concave (which occurs when at least one interior angle is greater than 180 degrees).

Therefore, the given quadrilateral, based on its properties and symmetry, is a convex deltoid.