Question

calculate the size of angle (x) in the pentagon below.

not drawn accurately

Explanation:

⚡ Using what you learned: properties of polygons

Step 1: Sum of exterior angles

The sum of the exterior angles of any convex polygon is always \( 360^\circ \).

Let's identify the exterior angles at each of the 5 vertices of the pentagon, going clockwise starting from the top-left:

1. Top-left vertex: \( 35^\circ \) (exterior angle)
2. Top-right vertex: \( 118^\circ \) (exterior angle)
3. Bottom-right vertex: \( 73^\circ \) (exterior angle)
4. Bottom-left vertex (with interior angle \( x \)): The exterior angle is \( 180^\circ - x \)
5. Middle-left vertex: \( 48^\circ \) (exterior angle)

Step 2: Set up the equation

Sum the exterior angles and set them equal to \( 360^\circ \):

$$ 35^\circ + 118^\circ + 73^\circ + (180^\circ - x) + 48^\circ = 360^\circ $$

Step 3: Solve for \( x \)

Combine the known values:

$$ 35 + 118 + 73 + 180 + 48 - x = 360 $$

$$ 454 - x = 360 $$

$$ x = 454 - 360 $$

$$ x = 94^\circ $$

Answer:

\( 94^\circ \)