We read your photo as:

A) The sum of the interior angles of a polygon is 1440^ exto. Calculate the number of sides of this polygon. b) The bar chart shows the number of learners who got distinctions in a test in each of the

Mathematics

ScanSolve AI Answer

Answers

2 parts
a

10 sides\text{10 sides}

b

FB and FD\text{FB and FD}

28 learners\text{28 learners}

Step-by-step solution

7 steps

Here are the solutions for the problems:

Part a· 2 steps

The sum of the interior angles of a polygon is 1440∘1440^\circ. Calculate the number of sides of this polygon.

  1. Recall the formula for the sum of interior angles of a polygon.

    The sum of the interior angles of a polygon with nn sides is given by the formula:

    Sum=(n−2)×180∘\text{Sum} = (n-2) \times 180^\circ

  2. Substitute the given sum into the formula and solve for nn.

    1440∘=(n−2)×180∘1440^\circ = (n-2) \times 180^\circ

    Divide both sides by 180∘180^\circ:

    1440180=n−2\frac{1440}{180} = n-2 8=n−28 = n-2

    Add 2 to both sides:

    n=8+2n = 8 + 2 n=10n = 10

    The polygon has 10 sides\boxed{\text{10 sides}}.

Part b

FB and FD\text{FB and FD}

The bar chart below shows the number of learners who got distinctions in a test in each of the Grade 9 classes.

b)(i) Find the modal class.

  1. Understand what a modal class is.

    The modal class is the class with the highest frequency, meaning the class with the most learners who got distinctions.

  2. Read the number of learners for each class from the bar chart.

    • Class FA: 4 learners
    • Class FB: 8 learners
    • Class FC: 6 learners
    • Class FD: 8 learners
    • Class FE: 2 learners

  3. Identify the class(es) with the highest number of learners.

    Both Class FB and Class FD have 8 learners, which is the highest number.
    The modal class is FB and FD\boxed{\text{FB and FD}}.

    b)(ii) Total number of learners who got distinctions.

  4. Sum the number of learners from all classes.

    Total learners = (Learners in FA) + (Learners in FB) + (Learners in FC) + (Learners in FD) + (Learners in FE)

    Total=4+8+6+8+2\text{Total} = 4 + 8 + 6 + 8 + 2

  5. Perform the addition.

    Total=12+6+8+2\text{Total} = 12 + 6 + 8 + 2 Total=18+8+2\text{Total} = 18 + 8 + 2 Total=26+2\text{Total} = 26 + 2 Total=28\text{Total} = 28

    The total number of learners who got distinctions is 28 learners\boxed{\text{28 learners}}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QA regular polygon has one of its interior angles as 144°. a) Name the polygon. b) Find the number of…QThe sum of the interior angles of a polygon is 1980^ exto. Find the number of sides the polygon has…QIf the interior angle of a regular polygon has 150 degrees, how many sides does the polygon have?…QA polygon has an interior angle sum of 1260^. Calculate the number of sides it has.QIf the sum of interior angles of a regular polygon is 2340, 340. Find the number of side
Browse by topic:StatisticsGeometry
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.