Question

In the figure, it is known , $\angle$CBA = 60 ${}^{\circ }$ and $\angle$BCA = 40 ${}^{\circ }$. What is the value of $\angle$CAO ?

• A. 120 ${}^{\circ }$
  
• B. 80 ${}^{\circ }$
  
• C. 100 ${}^{\circ }$
  
• D. 60 ${}^{\circ }$

Answer 1

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


We know, the sum of all the angles in a triangles is 180 ${}^{\circ }$ ( Legendre's axiom).

$\therefore$
$\angle$CBA + $\angle$BCA + $\angle$CAB = 180 ${}^{\circ }$
$\Rightarrow$ 40 ${}^{\circ }$ + 60 ${}^{\circ }$ + $\angle$CAB = 180 ${}^{\circ }$
$\Rightarrow$ $\angle$CAB = 80 ${}^{\circ }$

Since, O,A and B lie on the same line,
$\angle$CAB + $\angle$CAO = 180 ${}^{\circ }$
$\Rightarrow$ $\angle$CAO = 100 ${}^{\circ }$