In the diagram below, find the value of x.

Question 4: Step 1: Analyze the given triangle. The diagram shows a triangle with sides AB = 5 cm, BC = 5 cm, and AC = $x$ cm. Sides AB and BC have double tick marks, indicating they are equal in length. Side AC has a single tick mark. In basic geometry problems where a specific value for $x$ is expected without additional information (like angles), different tick marks on all sides often imply that all sides are equal, making it an equilateral triangle. We will proceed with this common interpretation to find a unique value for $x$.

Step 2: Determine the value of $x$. If the triangle is equilateral, all its sides are equal in length. Therefore, $AC = AB = BC$. $x = 5 \text{ cm}$ The value of $x$ is $\boxed{\text{5 cm}}$.

Question 5: a) Find the value of $x$ in the first triangle. Step 1: Identify the angles in the first triangle. The diagram shows a large right-angled triangle. The square symbol indicates a $90^\circ$ angle at the bottom left vertex. The angle at the top vertex is split into two parts: $45^\circ$ and $30^\circ$. The angle at the bottom right vertex is $x$. The total angle at the top vertex is $45^\circ + 30^\circ = 75^\circ$.

Step 2: Apply the angle sum property of a triangle. The sum of the interior angles in any triangle is $180^\circ$. $90^\circ + 75^\circ + x = 180^\circ$

Step 3: Solve for $x$. $165^\circ + x = 180^\circ$ $x = 180^\circ - 165^\circ$ $x = 15^\circ$ The value of $x$ is $\boxed{\text{15}}$.

b) Find the value of $x$ in the second triangle. Step 1: Identify the angles in the second triangle. The diagram shows a right-angled triangle. One angle is $x^\circ$, another is $60^\circ$, and the third angle is $90^\circ$ (indicated by the square symbol).

Step 2: Apply the angle sum property of a triangle. The sum of the interior angles in any triangle is $180^\circ$. $x^\circ + 60^\circ + 90^\circ = 180^\circ$

Step 3: Solve for $x$. $x^\circ + 150^\circ = 180^\circ$ $x^\circ = 180^\circ - 150^\circ$ $x^\circ = 30^\circ$ The value of $x$ is $\boxed{\text{30}}$.