Question

In the following figure,

$\angle$1 = 50${}^{\circ }$, $\angle$2 = 80${}^{\circ }$, $\angle$3 = 70${}^{\circ }$ and
$\angle$4 = 60${}^{\circ }$. What is the value of $\angle$5 +$\angle$6?

• A. 120${}^{\circ }$
• B. 90${}^{\circ }$
• C. 100${}^{\circ }$
• D. 80${}^{\circ }$

Answer 1

The correct option is C 100${}^{\circ }$

It can be observed that
$\angle$1, $\angle$3 and $\angle$5 are the angles of a triangle.
From Legendre's axiom, we can say
$\angle$1 + $\angle$3 + $\angle$5 = 180${}^{\circ }$
$\Rightarrow$$\angle$5 + 50${}^{\circ }$ + 70${}^{\circ }$ = 180${}^{\circ }$
$\Rightarrow$$\angle$5 = 60${}^{\circ }$
Similarly, it can also be observed
$\angle$2, $\angle$4 and $\angle$6 are the angles of a triangle.
From Legendre's axiom, we can say
$\angle$2 + $\angle$4 + $\angle$6 = 180${}^{\circ }$
$\Rightarrow$$\angle$6 + 80${}^{\circ }$ + 60${}^{\circ }$ = 180${}^{\circ }$
$\Rightarrow$$\angle$6 = 40${}^{\circ }$
$\therefore$ $\angle$5 + $\angle$6 = 60${}^{\circ }$ + 40${}^{\circ }$
$\Rightarrow$$\angle$5 + $\angle$6 = 100${}^{\circ }$