Points and lines are geometry's most basic building blocks, and, somewhat surprisingly, they're deliberately left as undefined primitive terms rather than formally defined in terms of anything simpler, since geometry has to start somewhere, and starting concepts can't be defined using concepts that don't yet exist. An angle, by contrast, is built directly out of these two undefined primitives: it's the figure formed where two lines, or line segments, meet at a shared point, and every other geometric object and every angle measurement is ultimately constructed out of relationships between these two undefined starting concepts.
Leaving points and lines undefined isn't sloppiness, it's a deliberate logical necessity
Any formal system built on definitions has to stop somewhere, since defining every single term in terms of some other term would either run in an endless, unproductive circle or never actually terminate at all. Euclidean geometry handles this by explicitly designating points and lines as primitive, undefined terms, working instead entirely from their described properties and the relationships allowed between them, a point has no size or dimension, a line extends infinitely in both directions, rather than from any formal definition of what a point or a line actually "is" at some more fundamental level.
Angles, and everything built from them, rest entirely on these two undefined primitives
An angle is formed wherever two lines or line segments share a common point, and its measure captures how much rotation separates the two lines around that shared point, a genuinely precise geometric relationship built entirely out of points and lines with no further undefined terms needed. From this single building block, angle, an enormous amount of further geometry follows, triangle interior angles, parallel line relationships, polygon interior angle sums, all of it ultimately traceable back down to nothing more than points, lines and the specific angular relationships defined directly between them.
What we're still unsure about
That points and lines function as undefined primitive terms, with angles and every further geometric concept built up from their described relationships, is well established, rigorously formalised geometry going back over two thousand years to Euclid's original axiomatic treatment. What's more genuinely a matter of ongoing foundational refinement is exactly how completely Euclid's own original list of properties and axioms actually pins down points' and lines' allowed behaviour without any hidden gaps, since later mathematicians found that Euclid's original axioms needed real, careful supplementing to be fully logically rigorous by modern standards, and the history of that supplementing is itself an active area of study in the history and foundations of mathematics.
This sits inside Points, Lines & Angles, one of eight topics in Geometry, one of seven domains in Mathematics, one of seventeen subjects the app can quiz you on.