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Find the letters angles in the shape below.

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Part 34· 2 steps

Find the lettered angle in the shape below.

  1. Identify the relationship between the angles.

    The angles aa and 75∘75^\circ are angles on a straight line, which sum to 180∘180^\circ.

    a+75∘=180∘a + 75^\circ = 180^\circ

  2. Solve for aa.

    a=180∘−75∘a = 180^\circ - 75^\circ a=105∘a = 105^\circ

    The correct option is (a).
    The lettered angle is 105∘\boxed{\text{105}^\circ}.

Part 35· 2 steps

4 numbers added together and the result is 96. If 3 of the numbers are 22.5, 23.5 and 24.5 respectively. Find the fourth number.

  1. Sum the three known numbers.

    Sum of known numbers=22.5+23.5+24.5\text{Sum of known numbers} = 22.5 + 23.5 + 24.5 Sum of known numbers=70.5\text{Sum of known numbers} = 70.5

  2. Subtract the sum of known numbers from the total sum to find the fourth number.

    Fourth number=96−70.5\text{Fourth number} = 96 - 70.5 Fourth number=25.5\text{Fourth number} = 25.5

    The correct option is (c).
    The fourth number is 25.5\boxed{\text{25.5}}.

Part 36· 3 steps

The area of a circle is 154 cm². Find the radius.

  1. Use the formula for the area of a circle.

    The area of a circle is A=πr2A = \pi r^2. Given A=154 cm2A = 154\, \text{cm}^2 and using π=227\pi = \frac{22}{7}.

    154=227r2154 = \frac{22}{7} r^2

  2. Solve for r2r^2.

    r2=154×722r^2 = \frac{154 \times 7}{22} r2=7×7r^2 = 7 \times 7 r2=49r^2 = 49

  3. Find the radius rr.

    r=49r = \sqrt{49} r=7 cmr = 7\, \text{cm}

    The correct option is (b).
    The radius is 7 cm\boxed{\text{7 cm}}.

Part 37· 2 steps

A man sold an article for N980 and lose 25%. Find the cost price of the article.

  1. Determine the selling price as a percentage of the cost price.

    If there is a 25% loss, the selling price (SP) is 100%−25%=75%100\% - 25\% = 75\% of the cost price (CP).

    SP=0.75×CP\text{SP} = 0.75 \times \text{CP}

  2. Calculate the cost price.

    Given SP = N980.

    980=0.75×CP980 = 0.75 \times \text{CP} CP=9800.75\text{CP} = \frac{980}{0.75} CP=1306.67\text{CP} = 1306.67

    None of the options (a) N1,445, (b) N1,325, (c) N1,245, (d) N1,225 match the calculated cost price.
    The cost price of the article is N1306.67\boxed{\text{N1306.67}}.

Part 38· 2 steps

Divide 25.8 by 1.5 and leave your answer to 2 decimal points.

  1. Perform the division.

    25.81.5=17.2\frac{25.8}{1.5} = 17.2

  2. Express the answer to two decimal points.

    17.2017.20

    None of the options (a) 10.15, (b) 10.19, (c) 10.18, (d) 16.72 match the calculated value.
    The result is 17.20\boxed{\text{17.20}}.

Part 39· 2 steps

Aman celebrated his 90th birthday in 2022. What year was he born?

  1. Subtract the age from the current year.

    Birth year=Current year−Age\text{Birth year} = \text{Current year} - \text{Age} Birth year=2022−90\text{Birth year} = 2022 - 90

  2. Calculate the birth year.

    Birth year=1932\text{Birth year} = 1932

    The correct option is (c).
    He was born in 1932\boxed{\text{1932}}.

Part 40· 2 steps

In a class of 40 students, 3/5 of them had paid their school fees. How many students are left to pay their school fees?

  1. Calculate the number of students who paid their fees.

    Number paid=35×40\text{Number paid} = \frac{3}{5} \times 40 Number paid=3×8\text{Number paid} = 3 \times 8 Number paid=24\text{Number paid} = 24

  2. Calculate the number of students left to pay.

    Number left to pay=Total students−Number paid\text{Number left to pay} = \text{Total students} - \text{Number paid} Number left to pay=40−24\text{Number left to pay} = 40 - 24 Number left to pay=16\text{Number left to pay} = 16

    The correct option is (b).
    16 students\boxed{\text{16 students}} are left to pay their school fees.

Part 41· 2 steps

It took 5 boys 6 days to do a piece of work. How many days will it take 3 boys to do the same piece of work?

  1. Use the inverse proportion relationship.

    The total amount of work is constant. If BB is the number of boys and DD is the number of days, then B1D1=B2D2B_1 D_1 = B_2 D_2.

    5 boys×6 days=3 boys×D2 days5\, \text{boys} \times 6\, \text{days} = 3\, \text{boys} \times D_2\, \text{days} 30=3D230 = 3 D_2

  2. Solve for D2D_2.

    D2=303D_2 = \frac{30}{3} D2=10 daysD_2 = 10\, \text{days}

    The correct option is (d).
    It will take 10 days\boxed{\text{10 days}} for 3 boys to do the same piece of work.

Part 42· 2 steps

Find the mode of this data: 2, 0, 0, 1, 0, 3, 4, 5.

  1. Count the frequency of each number in the data set.

    • 0 appears 3 times.
    • 1 appears 1 time.
    • 2 appears 1 time.
    • 3 appears 1 time.
    • 4 appears 1 time.
    • 5 appears 1 time.

  2. Identify the number with the highest frequency.

    The number 0 appears most frequently (3 times).
    The correct option is (b).
    The mode of the data is 0\boxed{\text{0}}.

Part 43

The number(s) that appear in the middle of a given data is called

The number(s) that appear in the middle of an ordered data set is called the Median.
The correct option is (c).
The answer is Median\boxed{\text{Median}}.

Part 44· 2 steps

From the sum 1897 and 234, subtract 2089.

  1. Calculate the sum of 1897 and 234.

    1897+234=21311897 + 234 = 2131

  2. Subtract 2089 from the sum.

    2131−2089=422131 - 2089 = 42

    The correct option is (c).
    The result is 42\boxed{\text{42}}.

Part 45· 2 steps

Bola had N4,232 and Audu had N2,834. How much did Bola have more than Audu?

  1. Find the difference between Bola's money and Audu's money.

    Difference=N4232−N2834\text{Difference} = \text{N}4232 - \text{N}2834

  2. Calculate the difference.

    Difference=N1398\text{Difference} = \text{N}1398

    The correct option is (b).
    Bola had N1,398\boxed{\text{N1,398}} more than Audu.

Part 46· 2 steps

What is 7½ of 400?

  1. Convert 7½ to a decimal or improper fraction.

    712=7.57\frac{1}{2} = 7.5

  2. Multiply 7.5 by 400.

    7.5×400=30007.5 \times 400 = 3000

    The correct option is (b).
    7½ of 400 is 3000\boxed{\text{3000}}.

Part 47· 2 steps

If 2x−7=212x - 7 = 21, what is the value of x?

  1. Add 7 to both sides of the equation.

    2x−7+7=21+72x - 7 + 7 = 21 + 7 2x=282x = 28

  2. Divide both sides by 2.

    2x2=282\frac{2x}{2} = \frac{28}{2} x=14x = 14

    The correct option is (d).
    The value of xx is 14\boxed{\text{14}}.

Part 48

A line that runs from the center of a circle to any part of it is called

A line segment that runs from the center of a circle to any point on its circumference is called a Radius.
The correct option is (b).
The answer is Radius\boxed{\text{Radius}}.

Part 49· 1 step

Find the difference between 1000 and 418.

  1. Subtract 418 from 1000.

    1000−418=5821000 - 418 = 582

    The correct option is (d).
    The difference is 582\boxed{\text{582}}.

Part 50

The reverse of expansion is

The reverse process of expansion (multiplying out terms) in algebra is Factorization, where an expression is written as a product of its factors.
The correct option is (c).
The reverse of expansion is Factorization\boxed{\text{Factorization}}.

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