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

${190}^{\circ }$

(i) $\Delta$ ABC is isosceles (AB = AC)

(ii) $\therefore \angle ACB=\angle ABC={75}^{\circ }....$ (base angles of an isosceles)

(iii) $\therefore d={180}^{\circ }-{75}^{\circ }$...(linear pair)

= ${105}^{\circ }$

(iv) In $\Delta ADC$

${60}^{\circ }+a^{\circ }+b^{\circ }=d^{\circ }$ (exteriar angle theorem)

${60}^{\circ }+a^{\circ }+b^{\circ }={105}^{\circ }$

$a^{\circ }+b^{\circ }={45}^{\circ }$

(v) In $\Delta ACE$

$C^{\circ }+d^{\circ }={145}^{\circ }$... (exteriar angle theorem)

(vi) $\therefore a^{\circ }+b^{\circ }+c^{\circ }+d^{\circ }={45}^{\circ }+{145}^{\circ }...$ (from (iv) to (v)\)

= ${190}^{\circ }$