BTGmoderatorDC wrote:In isosceles triangle DEF, what is the measure of angle E?

(1) Angle D measures 42 degrees
(2) Angle F measures 96 degrees
Source: Veritas Prep

All measures are in degrees.

$$\Delta DEF\,\,{\rm{isosceles}}\,\,\,\,\left( * \right)$$
$${\rm{?}}\,\,{\rm{ = }}\,\,\angle {\rm{E}}$$
$$\left( 1 \right)\,\,\angle {\rm{D}}\,\,{\rm{ = }}\,\,{\rm{42}}\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {\angle {\rm{D}}\,{\rm{;}}\,\angle {\rm{E;}}\,\,\angle {\rm{F}}} \right)\,\, = \,\,\left( {42\,;\,42\,;96} \right)\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,{\rm{42}} \hfill \cr
\,{\rm{Take}}\,\,\left( {\angle {\rm{D}}\,{\rm{;}}\,\angle {\rm{E;}}\,\,\angle {\rm{F}}} \right)\,\, = \,\,\left( {42\,;69\,;69} \right)\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,{\rm{69}}\,\, \hfill \cr} \right.\,$$
$$\left( 2 \right)\,\,\angle {\rm{F}}\,\,{\rm{ = }}\,\,{\rm{96}}\,\,\,\left( { \ne \,\,\angle {\rm{D}}\,\,{\rm{and}}\,\, \ne \angle {\rm{E}}} \right)\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,\angle {\rm{D}}\,\, = \,\,\angle {\rm{E}}\,\,{\rm{ = }}\,\,{{{\rm{180}} - 96} \over 2}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\,$$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.