Question

In the given figure $\angle ACB={109}^{\circ }$ and $\angle CDE={31}^{\circ }$. The sum of a, b, f and g is

• A. ${360}^{\circ }$
• B. ${211}^{\circ }$
• C. ${140}^{\circ }$
• D. ${257}^{\circ }$

Answer 1

The correct option is B ${211}^{\circ }$

In the fig,

$ACB=ECD={109}^{\circ }$ --------- vertically opposite angles

In $△ABC$

$\angle A+\angle B+\angle C={180}^{\circ }$

$a+b={180}^{\circ }-{109}^{\circ }={71}^{\circ }$-------------(i)

In $△CED$

$\angle C+\angle D+\angle E={180}^{\circ }$

$\angle E={180}^{\circ }-{109}^{\circ }-{31}^{\circ }={40}^{\circ }$

$GEF=CED={40}^{\circ }$ --------- vertically opposite angles

In $△GEF$

$\angle G+\angle F+\angle E={180}^{\circ }$

$g+f={180}^{\circ }-{40}^{\circ }={140}^{\circ }$-------------(ii)

Adding (i) and (ii)

$a+b+g+f={71}^{\circ }-{140}^{\circ }={211}^{\circ }$

Option B.