Question

If the side of a triangle are produced as shown in the figure, then x + y + z = ____.

• A. 180°
• B. 360°
• C. 90°
• D. 270°

Answer 1

The correct option is B

360°

(i) $\angle \text{A}+\angle \text{B}+\angle \text{C}={180}^{\circ }\dots \dots \left(\text{Sum of angles of a}\Delta \right)$

(ii) $x=\angle \text{B}+\angle \text{C}\dots \dots \left(\text{Exterior angle theorem}\right)$

(iii) $y=\angle \text{A}+\angle \text{C}\dots \dots \left(\text{Exterior angle theorem}\right)$

(iv) $z=\angle \text{A}+\angle \text{B}\dots \dots \left(\text{Exterior angle theorem}\right)$

(v) $x+y+z=(\angle \text{A}+\angle \text{B}+\angle \text{C})$

$=2\left({180}^{\circ }\right)$

$={360}^{\circ }$