Question

The measures of angles of the rhombus given in the diagram are

• A. ${60}^{\circ },{120}^{\circ },{60}^{\circ }{120}^{\circ }$
  
• B. ${50}^{\circ },{130}^{\circ },{50}^{\circ }{130}^{\circ }$
  
• C. ${30}^{\circ },{150}^{\circ },{30}^{\circ }{150}^{\circ }$
  
• D. ${40}^{\circ },{140}^{\circ },{40}^{\circ }{140}^{\circ }$

Answer 1

The correct option is C

${30}^{\circ },{150}^{\circ },{30}^{\circ }{150}^{\circ }$

Each angle of square = ${90}^{\circ }$

For a regular hexagon n = 6

Each exterior angle $=\frac{360}{6}$

$={60}^{\circ }$

Internal angle + External angle $={180}^{\circ }$ (Linear pair)

$\Rightarrow i+e={180}^{\circ }$

$i+{60}^{\circ }={180}^{\circ }$

$\Rightarrow i={180}^{\circ }-{60}^{\circ }$

$i={120}^{\circ }$

Angle about a point = ${360}^{\circ }$

$\Rightarrow {90}^{\circ }+{120}^{\circ }+{120}^{\circ }+x^{\circ }={360}^{\circ }$

$\Rightarrow {330}^{\circ }+x^{\circ }={360}^{\circ }$

$\Rightarrow x^{\circ }={360}^{\circ }-{330}^{\circ }={30}^{\circ }$

$\therefore$ Angles of Rhombus are ${30}^{\circ },{150}^{\circ },{30}^{\circ }and{150}^{\circ }$