Question

En el triángulo

CAT,

tenemos

\angle ACT =\angle ATC

y

\angle CAT = 36^\circ.

Si

\overline{TR}

biseca

\angle ATC,

entonces

\angle CRT =

In triangle

CAT,

we have

\angle ACT =\angle ATC

and

\angle CAT = 36^\circ.

If

\overline{TR}

bisects

\angle ATC,

then

\angle CRT =

16^\circ

51^\circ

72^\circ

90^\circ

108^\circ

Primero halla los dos ángulos de la base iguales de

\triangle CAT.

First find the two equal base angles of

\triangle CAT

Usa la bisectriz del ángulo en

T.

Use the angle bisector at

T

Obtenemos

\begin{aligned} \angle CAT + \angle ATC \\ \quad {}+ \angle ACT &= 180 \\ 36 + 2 \cdot \angle ATC &= 180 \\ \angle ATC &= 72^{\circ}. \end{aligned}

Debido a la bisección, también sabemos que

\angle RTC = 72 \div 2 = 36^{\circ}.

Finalmente, vemos que

\begin{aligned} \angle RTC + \angle TCR \\ \quad {}+ \angle CRT &= 180 \\ 36 + 72 + \angle CRT &= 180 \\ \angle CRT &= 72^{\circ}. \end{aligned}

Así, C es la respuesta correcta.

We get

\begin{aligned} \angle CAT + \angle ATC \\ \quad {}+ \angle ACT &= 180 \\ 36 + 2 \cdot \angle ATC &= 180 \\ \angle ATC &= 72^{\circ}. \end{aligned}

Due to bisection, we also know that

\angle RTC = 72 \div 2 = 36^{\circ}.

Finally, we see that

\begin{aligned} \angle RTC + \angle TCR \\ \quad {}+ \angle CRT &= 180 \\ 36 + 72 + \angle CRT &= 180 \\ \angle CRT &= 72^{\circ}. \end{aligned}

Thus, C is the correct answer.