Question

In a triangle ABC , it is known, $\angle$A = 60 ${}^{\circ }$, $\angle$B = 90${}^{\circ }$. What is the value of $\angle$ACE?

• A. 160 ${}^{\circ }$
• B. 120 ${}^{\circ }$
• C. 150 ${}^{\circ }$
• D. 30 ${}^{\circ }$

Answer 1

The correct option is C 150 ${}^{\circ }$


Given,
$\angle$A = 60 ${}^{\circ }$, $\angle$B = 90${}^{\circ }$.
From Legendre's theorem, we know,
The sum of the values of all the angles in a triangle = 180${}^{\circ }$.
$\therefore$
$\angle$A + $\angle$B + $\angle$C = 180${}^{\circ }$
$\Rightarrow$ $\angle$C = 180${}^{\circ }$- 60${}^{\circ }$ - 90${}^{\circ }$
$\Rightarrow$ $\angle$C = 30${}^{\circ }$

$\because$ BCE is straight line, $\angle$ACB and $\angle$ACE form a linear pair.
$\Rightarrow$ $\angle$ACB + $\angle$ACE = 180${}^{\circ }$
$\Rightarrow$ $\angle$ACE = 150 ${}^{\circ }$