Question

The sides$BC$,$CA$ and $AB$ of $\Delta ABC$ are produced in order to form exterior angles $\angle ACD$,$\angle ABG$, and $\angle CAE$ then $\angle ACD+\angle CAE+\angle ABG$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$\Rightarrow$ $x+y+z={180}^{\circ }$

$\Rightarrow$ $\angle ACD+\angle CAE+\angle ABG$
$=({180}^{\circ }-z)+({180}^{\circ }-x)+({180}^{\circ }-y)$

$\Rightarrow$ $\angle ACD+\angle CAE+\angle ABG$
$={540}^{\circ }-(x+y+z)={540}^{\circ }-{180}^{\circ }={360}^{\circ }$