What are congruent angles?

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congruent angles are two angles that have the same measure in degrees, that is, the opening formed is the same.

O mathematical symbol used to indicate that two angles are congruent is ≅.

Example:

See the angle $\dpi{120} \mathrm{B\widehat{A}C}$ measures 42° and the angle $\dpi{120} \mathrm{D\widehat{E}F}$ also measures 42°, that is:

$\dpi{120} \mathrm{med (B\widehat{A}C) = 42^{\circ}}$

$\dpi{120} \mathrm{med (D\widehat{E}F) = 42^{\circ}}$

Therefore, they are congruent:

$\dpi{120} \mathrm{B\widehat{A}C \cong D\widehat{E}F}$

As you can see, the congruence of two angles doesn't have to do with their position on the plane being the same, they can be positioned differently and be congruent, as is the case with the angles of the example.

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Also, notice that when we compare the measurements of the congruent angles we use the equal symbol (=), because the measurements are equal. The symbol ≅ is only used when referring to the angles themselves.

Exercise:

the angles $\dpi{120} \mathrm{A\widehat{O}B}$ and $\dpi{120} \mathrm{P\widehat{O}Q}$ are congruent. Knowing that $\dpi{120} \mathrm{med (A\widehat{O}B) = x + 15^{\circ}}$ is that $\dpi{120} \mathrm{med (P\widehat{O}Q) = 75^{\circ}}$ , discover the value of $\dpi{120} \mathrm{x}$ .