CTET 2 Math and Science 07 Jul 2024 Paper

We have $\mathit{M}$ is a point on side $\mathit{A}\mathit{B}$ of a triangle $\mathit{A}\mathit{B}\mathit{C}$ such that $\mathit{A}\mathit{M}=\mathit{B}\mathit{M}=\mathit{C}\mathit{M}$.
If angles A and B are respectively x and ${70}^{\circ }$
Now
By isosceles triangle -

$\angle \mathit{A}\mathit{C}\mathit{B}=\angle \mathit{A}\mathit{C}\mathit{M}+\angle \mathit{M}\mathit{C}\mathit{B}$


$\angle \mathit{A}\mathit{C}\mathit{B}=\mathit{x}+{70}^{\circ }$
Now use the triangle property -
$\angle \mathit{C}\mathit{A}\mathit{M}+\angle \mathit{C}\mathit{B}\mathit{M}+\angle \mathit{A}\mathit{C}\mathit{B}=180$
$\Rightarrow \mathit{x}+70+\mathit{x}+70=180$
$\Rightarrow 2\mathit{x}+140=180$
$\Rightarrow 2\mathit{x}=180-140$
$\Rightarrow 2\mathit{x}=40$
$\Rightarrow \mathit{x}=20$
Now $3\mathit{x}+{25}^{\circ }=3\times 20+25$
$=60+25={85}^{\circ }$