The pie chart below shows the major expenditure from Mr Kataala's income for a month in 2019. Study it carefully and answer the questions that follow. (a) Calculate the value of x. (b) If he spent sh. 272000 on masks, find his monthly income.

Add the given angles for Masks, Sanitizers, and Gloves:

The value of $x$ is $\boxed{45}$.

Angle for Masks $= (x+40)^\circ = (45+40)^\circ = 85^\circ$.

The expenditure on Masks (sh. 272000) corresponds to $85^\circ$ of the total $360^\circ$ income.
Let $M$ be the total monthly income.

His monthly income is $\boxed{\text{sh.1,152,000}}$.

31. Study the figure below and answer the questions that follow.
(Assuming the question asks for the values of $x$ and $k$.)

The single dash marks on AD and DB indicate that $AD = DB$. Therefore, $\triangle ADB$ is an isosceles triangle, which means $\angle DAB = \angle DBA$. Let's call this angle $\alpha$. So, $\angle DAB = \alpha$ and $\angle DBA = \alpha$.
The double dash marks on AB and BC indicate that $AB = BC$. Therefore, $\triangle ABC$ is an isosceles triangle, which means $\angle BAC = \angle BCA$.

From Step 1, $\angle BAC = \angle DAB = \alpha$.
Since $\angle BAC = \angle BCA$, we have $\angle BCA = \alpha$.
From the diagram, $\angle BCA = x$. Therefore, $x = \alpha$.
So, in $\triangle ADB$, $\angle DAB = x$ and $\angle DBA = x$.

The sum of angles in $\triangle DBC$ is $180^\circ$.

From $\triangle ABC$ being isosceles with $\angle BAC = x$ and $\angle BCA = x$:

Also, from the diagram, $\angle ABC$ is the sum of $\angle DBA$ and $\angle DBC$:

Since $\angle DBA = x$ (from Step 2) and $\angle DBC = k$:

Substitute equation (2) into equation (1):

Now substitute $x = 20^\circ$ back into equation (1) to find $k$:

The value of $x$ is $\boxed{20^\circ}$ and the value of $k$ is $\boxed{120^\circ}$.