Question

In a triangle ABC , it is known $\angle$A = 45 ${}^{\circ }$ and $\angle$B = 75 ${}^{\circ }$. What is the value of $\angle$C ?

• A. 45 ${}^{\circ }$
• B. 65 ${}^{\circ }$
• C. 60 ${}^{\circ }$
• D. 55 ${}^{\circ }$

Answer 1

The correct option is C 60 ${}^{\circ }$

We know, from Legendre's Axiom, the sum of all the angles in a triangle is equal to two right angles.

$\Rightarrow$ $\angle$A + $\angle$B + $\angle$C = 180${}^{\circ }$
$\Rightarrow$ 45${}^{\circ }$ + 75${}^{\circ }$ + $\angle$C = 180${}^{\circ }$
$\Rightarrow$ $\angle$C = 60${}^{\circ }$