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In the diagram below X is

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3 parts
4

5 cm\text{5 cm}

5

15\text{15}

6

30\text{30}

Step-by-step solution

8 steps

Part 4· 2 steps

  1. Analyze the given triangle.

    The diagram shows a triangle with sides AB = 5 cm, BC = 5 cm, and AC = xx 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 xx 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 xx.

  2. Determine the value of xx.

    If the triangle is equilateral, all its sides are equal in length.
    Therefore, AC=AB=BCAC = AB = BC.

    x=5 cmx = 5 \text{ cm}

    The value of xx is 5 cm\boxed{\text{5 cm}}.

Part 5

15\text{15}

Find the value of xx in the triangle below.

  1. Identify the angles in the first triangle under question 5.

    The diagram shows a large right-angled triangle. The square symbol indicates a 90∘90^\circ angle at the bottom left vertex. The angle at the top vertex is split into two parts: 45∘45^\circ and 30∘30^\circ. The angle at the bottom right vertex is xx.
    The total angle at the top vertex is 45∘+30∘=75∘45^\circ + 30^\circ = 75^\circ.

  2. Apply the angle sum property of a triangle.

    The sum of the interior angles in any triangle is 180∘180^\circ.

    90∘+75∘+x=180∘90^\circ + 75^\circ + x = 180^\circ
  3. Solve for xx.

    165∘+x=180∘165^\circ + x = 180^\circ x=180∘−165∘x = 180^\circ - 165^\circ x=15∘x = 15^\circ

    The value of xx is 15\boxed{\text{15}}.

Part 6

30\text{30}

Find the value of xx in the triangle below.

  1. Identify the angles in the triangle under question 6.

    The diagram shows a right-angled triangle. One angle is x∘x^\circ, another is 60∘60^\circ, and the third angle is 90∘90^\circ (indicated by the square symbol).

  2. Apply the angle sum property of a triangle.

    The sum of the interior angles in any triangle is 180∘180^\circ.

    x∘+60∘+90∘=180∘x^\circ + 60^\circ + 90^\circ = 180^\circ
  3. Solve for xx.

    x∘+150∘=180∘x^\circ + 150^\circ = 180^\circ x∘=180∘−150∘x^\circ = 180^\circ - 150^\circ x∘=30∘x^\circ = 30^\circ

    The value of xx is 30\boxed{\text{30}}.

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