Question

Find the value of $a+b+c+d$ in the following figure.

• A. ${200}^{\circ }$
• B. ${190}^{\circ }$
• C. ${180}^{\circ }$
• D. ${170}^{\circ }$

Answer 1

The correct option is B

${190}^{\circ }$

In $\Delta ABC$, $\angle ACB={75}^{\circ }$

$\therefore b={180}^{\circ }-({75}^{\circ }+{75}^{\circ })={30}^{\circ }$

In $\Delta ADB$,

$a+{60}^{\circ }={75}^{\circ }$ [Exterior angle property]

$a={15}^{\circ }$

In $\Delta ABC$, $d={75}^{\circ }+b$ [Exterior angle property]

$d={75}^{\circ }+{30}^{\circ }={105}^{\circ }$

In $\Delta ACE$, ${145}^{\circ }=c+d$ [Exterior angle property]

$c={145}^{\circ }-{105}^{\circ }={40}^{\circ }$

$\therefore a+b+c+d={15}^{\circ }+{30}^{\circ }+{40}^{\circ }+{105}^{\circ }={190}^{\circ }$