Question

A square has vertices A B C D labelled clockwise. An equilateral triangle is
constructed with labels A E C labelled clockwise. What is the size of angle C B E in
degrees?
options
(A) 30 (B) 45 (C) 135
(D) 145 (E) 150

Answer 1

$ABCD \: is \: a \: square . AEC \: is \: an \\equilateral \:triangle .$

$\angle {CBA } = 90\degree \: --(1)$

$Reflex angle \angle {CBA} = 360\degree - \angle {CBA } \\= 360\degree - 90\degree \\= 270\degree \: --(2)$

$Now, in \: \triangle {CBE} \: and \: \triangle {ABE}$

$BC = BA \: ( side ) \\CE = EA \: (side ) \\BE = BE \: ( Common \:side )$

$\triangle {CBE} \cong \triangle {ABE}$

$\angle {CBE } = \angle {ABE } \: \blue ( C.P.C.T )$

$\therefore \angle {CBE } = \frac{1}{2} \times Reflex angle \angle {CBA} \\= \frac{270}{2} \\= 135 \degree$

$Option \: \pink { ( C ) } \:is \: correct .$

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