Question

Find the value of x, y and z in the adjoining figure.

• A. $x=160$, $y=60$, $z=80$
• B. $x=60$, $y=80$, $z=40$
• C. $x=80$, $y=60$, $z=140$
• D. $x=140$, $y=80$, $z=60$

Answer 1

The correct option is C $x=80$, $y=60$, $z=140$

$In△BCE$

$⟹\angle BEC+\angle BCE+\angle CBE={180}^{\circ }$

$⟹{90}^{\circ }+{30}^{\circ }+\angle CBE={180}^{\circ }$

$⟹\angle CBE={60}^{\circ }$

$y={60}^{\circ }$

$In△APC:$

$⟹{50}^{\circ }+{30}^{\circ }+\angle APC={180}^{\circ }$

$⟹\angle APC={100}^{\circ }$

$\therefore x=180-\angle APC$

$(\because sumofanglesonastraightline={180}^{\circ })$

$⟹x={180}^{\circ }-{100}^{\circ }={80}^{\circ }$

$In△BOP:$

$z=x+y(exteriorangleofatriangle=sumoftwooppositeinteriorangles)$

$⟹z=80+60={140}^{\circ }$

$\therefore x={80}^{\circ },y={60}^{\circ },z={140}^{\circ }$