Question

In the given figure, find the measure of Angle DEF ?​

Answer 1

$Given , In \: \triangle DEF , \angle D = 2x + 38,\\\angle F = 68\degree ,\red{ \angle E = ? }$

$and, In \: \triangle ABC , \angle A = 4x,\\\angle C = 68\degree ,\red{ \angle B = ? }$

$In \: \triangle DEF \:and \: \triangle ABC$

$EF = BC ( side)$

$\angle F = \angle C ( Angle )$

$DF = AC \: (side)$

$\therefore \triangle DEF \cong \triangle ABC$

$\blue{ ( By \: SAS \: congruence \: rule )}$

$\angle D = \angle A \: \green { ( C.PC.T )}$

$\implies 2x + 38 = 4x$

$\implies 38 = 4x - 2x$

$\implies 38 = 2x$

$\implies x = \frac{38 }{2}$

$\implies x = 19 \: --(1)$

/* By Angle Sum Property */

$\angle D + \angle E + \angle F = 180\degree </p><p>[tex] </p><p>[tex]\implies 2x + 38 + \angle E + 68 = 180$

$\implies 2\times 19 + 38+ \angle E + 68 = 180$

$\implies 38 + 38 + \angle E + 68 = 180$

$\implies 144 + \angle E = 180$

$\implies \angle E = 180 - 144$

$\implies \angle E = 36 \degree$

Therefore.,

$\red{ Value \:of \:\angle {DEF} } \green { = 36 \degree}$

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