Question

Find the value of x + y + z.

• A. ${90}^{\circ }$
• B. ${180}^{\circ }$
• C. ${270}^{\circ }$
• D. ${360}^{\circ }$

Answer 1

The correct option is D ${360}^{\circ }$

Since sum of linear pair angles is ${180}^{\circ }$

$\therefore {90}^{\circ }+x={180}^{\circ }$

$\Rightarrow {90}^{\circ }+x={180}^{\circ }$

$\Rightarrow x={180}^{\circ }-{90}^{\circ }={90}^{\circ }$


$\text{And}z+{30}^{\circ }={180}^{\circ }$

$\Rightarrow z={180}^{\circ }-{30}^{\circ }={150}^{\circ }$

$\text{Also}y={90}^{\circ }+{30}^{\circ }={120}^{\circ }\text{[Exterior angle}$
$\text{property]}$

$\therefore x+y+z={90}^{\circ }+{120}^{\circ }+{150}^{\circ }={360}^{\circ }$