Angle Sum Property of a Triangle

In a $△PQR$, if $\angle P= 4\angle Q = 6\angle R = 2,$ calculate the angles.

"Note: The question given in the book seems to have some errors, the modified question is:"

In a $△PQR$, if $6\angle P= 3\angle Q= 2\angle R$, calculate the angles.

In the given figure, what are the measures of$x$ and $y$?

The ratio of three angles of a triangle is $1:2:3.$ What are the measure of the three angles of triangle?

In $△XYZ,$ $\angle X=40°,\angle Y=80°$ and the bisector of $\angle Y$and $\angle Z$meet at $O$. Find $\angle Z$.

In a $△DEF,$ $\angle E=70°$ and $\angle F=60°$. The bisector of $\angle F$ meets $DE$ at $G.$ If $k$ equals the difference between $\angle DGF$ and $\angle EGF$, then find the value of $k$.

The angles of a triangle are $\left(x-40\right)°, \left(x-20\right)°$ and $\left(\frac{1}{2}x-10\right)°$. Find the value of $x.$

If $\angle A+\angle B+\angle C+\angle D+\angle E+\angle F=k°$, then find the value of $k$. 

In the given figure $DE\parallel BC$, what is the value of $x$?