En un rectángulo, cada ángulo es recto.

Here en means something like in or within the figure.

So En un rectángulo means In a rectangle or In any rectangle.

In maths and geometry, Spanish often uses en this way:

• En un triángulo...
• En un círculo...
• En un cuadrado...

It introduces a general fact about that shape.

Un rectángulo is used because the sentence is talking about any rectangle, not one specific rectangle.

• En un rectángulo... = in a rectangle / in any rectangle
• En el rectángulo... = in the rectangle, meaning a specific rectangle already mentioned

So the indefinite article un gives a general, definition-like meaning.

Because cada is followed by a singular noun in Spanish.

So:

• cada ángulo = each angle / every angle
• not cada ángulos

More examples:

• cada día
• cada persona
• cada lado

This is different from English, where every also takes a singular noun: every angle.

Because cada normally goes directly before the noun.

So you say:

• cada ángulo
• cada lado
• cada estudiante

Not:

• cada el ángulo
• cada un ángulo

If you wanted to say each one of the angles, you could say:

• cada uno de los ángulos

But in your sentence, cada ángulo is the normal form.

Because the subject is grammatically singular: cada ángulo.

Even though cada ángulo refers to all the angles one by one, Spanish treats it as singular:

• Cada ángulo es recto
• Cada lado mide...
• Cada alumno tiene...

So the verb must be singular:

• es, not son

Because recto agrees with ángulo, and ángulo is a masculine singular noun.

So:

• ángulo recto
• cada ángulo es recto

If the noun were feminine singular, the adjective would change:

• línea recta

And if it were plural:

• ángulos rectos

This is normal adjective agreement in Spanish.

Good question. Recto can mean straight in some contexts, but in geometry it also means right in the sense of a 90-degree angle.

So:

• ángulo recto = right angle

In this sentence, recto does not mean morally upright or physically straight. It means the angle is a right angle.

That is why cada ángulo es recto means that every angle in a rectangle is 90 degrees.

Yes, you could. That version is grammatically correct.

• Cada ángulo es recto
• Cada ángulo es un ángulo recto

The version in your sentence is shorter and more natural in a simple definition or description.

Spanish often uses an adjective after ser instead of repeating the noun:

• El cielo es azul
• La mesa es redonda
• Cada ángulo es recto

Ángulo is the geometric term: angle.

Esquina usually means corner, especially in everyday language or in physical spaces:

• la esquina de la calle = the street corner
• la esquina de la mesa = the corner of the table

In geometry, ángulo is the correct word here because the sentence is talking about the mathematical angle, not just a corner.

The written accents show where the stress falls.

• rectángulo → stress on tán
• ángulo → stress on án

Without the accents, a Spanish speaker would expect the stress in a different place based on normal spelling rules.

So the accents are there to mark the correct pronunciation:

• re-TÁN-gu-lo
• ÁN-gu-lo

A rough English-friendly guide is:

en oon rek-TAHN-goo-lo, KAH-dah AHN-goo-lo es REK-toh

More carefully:

• En = like en in ten, but shorter
• un = close to oon
• rectángulo = re-TÁN-gu-lo
• cada = KA-da
• ángulo = ÁN-gu-lo
• es = short es
• recto = REK-to

In Spain, c before a in cada is a normal k sound.

Not really. The sentence can be written with or without it:

• En un rectángulo, cada ángulo es recto.
• En un rectángulo cada ángulo es recto.

Because En un rectángulo is a short introductory phrase, many writers would actually omit the comma. With the comma, there is just a slightly clearer pause.

So the version with the comma is understandable and acceptable, but without it is also very common.

It would be understood everywhere in the Spanish-speaking world.

The words:

• rectángulo
• ángulo
• recto

are standard mathematical Spanish, not something specific to Spain.

So this sentence works perfectly well in Spain and in Latin America.