We are asked to determine the size of the angle $x$ in each of the six diagrams.

1. Problem Description

We are asked to determine the size of the angle $x$ in each of the six diagrams.

2. Solution Steps

a) The diagram shows a right angle, which is $90^{\circ}$. The angle is divided into two angles, $36^{\circ}$ and $x^{\circ}$. Therefore, we have:

$x + 36 = 90$

$x = 90 - 36$

$x = 54$

b) The diagram shows a right angle, which is $90^{\circ}$. The angle is divided into two angles, $22^{\circ}$ and $x^{\circ}$. Therefore, we have:

$x + 22 = 90$

$x = 90 - 22$

$x = 68$

c) The diagram shows a straight line, and an angle that looks like a right angle ($90^{\circ}$). The straight line means the total degrees around the bottom angle is $180^{\circ}$. Therefore, we have:

$x + 73 = 90$

$x = 90 - 73$

$x = 17$

d) The angles $113^{\circ}$ and $x^{\circ}$ are supplementary, which means they add up to $180^{\circ}$. Therefore, we have:

$x + 113 = 180$

$x = 180 - 113$

$x = 67$

e) The diagram shows a right angle, which is $90^{\circ}$. The angle is divided into two angles, $x^{\circ}$ and $y^{\circ}$. Also, $x^{\circ}$ and $35^{\circ}$ form a right angle. Therefore, we have:

$x + 35 = 90$

$x = 90 - 35$

$x = 55$

f) The two angles labeled $x$ are vertical angles, which means they are equal. The angles $x$ and $50^{\circ}$ form a straight line.

$x + x + 50 = 180$

$2x + 50 = 180$

$2x = 180 - 50$

$2x = 130$

$x = \frac{130}{2}$

$x = 65$

3. Final Answer

a) $x = 54$

b) $x = 68$

c) $x = 17$

d) $x = 67$

e) $x = 55$

f) $x = 65$