Find the letters angles in the shape below.

Here are the solutions to the questions: Question 34: Find the lettered angle in the shape below. Step 1: Identify the relationship between the angles. The angles a and 75^ are angles on a straight line, which sum to 180^. a + 75^ = 180^ Step 2: Solve for a. a = 180^ - 75^ a = 105^ The correct option is (a). The lettered angle is 105^. Question 35: 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. Step 1: Sum the three known numbers. Sum of known numbers = 22.5 + 23.5 + 24.5 Sum of known numbers = 70.5 Step 2: Subtract the sum of known numbers from the total sum to find the fourth number. Fourth number = 96 - 70.5 Fourth number = 25.5 The correct option is (c). The fourth number is 25.5. Question 36: The area of a circle is 154 cm². Find the radius. Step 1: Use the formula for the area of a circle. The area of a circle is A = r^2. Given A = 154\, cm^2 and using = (22)/(7). 154 = (22)/(7) r^2 Step 2: Solve for r^2. r^2 = (154 × 7)/(22) r^2 = 7 × 7 r^2 = 49 Step 3: Find the radius r. r = sqrt(49) r = 7\, cm The correct option is (b). The radius is 7 cm. Question 37: A man sold an article for N980 and lose 25%. Find the cost price of the article. Step 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\% of the cost price (CP). SP = 0.75 × CP Step 2: Calculate the cost price. Given SP = N980. 980 = 0.75 × CP CP = (980)/(0.75) 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. Question 38: Divide 25.8 by 1.5 and leave your answer to 2 decimal points. Step 1: Perform the division. (25.8)/(1.5) = 17.2 Step 2: Express the answer to two decimal points. 17.20 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. Question 39: Aman celebrated his 90th birthday in 2022. What year was he born? Step 1: Subtract the age from the current year. Birth year = Current year - Age Birth year = 2022 - 90 Step 2: Calculate the birth year. Birth year = 1932 The correct option is (c). He was born in 1932. Question 40: 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? Step 1: Calculate the number of students who paid their fees. Number paid = (3)/(5) × 40 Number paid = 3 × 8 Number paid = 24 Step 2: Calculate the number of students left to pay. Number left to pay = Total students - Number paid Number left to pay = 40 - 24 Number left to pay = 16 The correct option is (b). 16 students are left to pay their school fees. Question 41: 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? Step 1: Use the inverse proportion relationship. The total amount of work is constant. If B is the number of boys and D is the number of days, then B_1 D_1 = B_2 D_2. 5\, boys × 6\, days = 3\, boys × D_2\, days 30 = 3 D_2 Step 2: Solve for D_2. D_2 = (30)/(3) D_2 = 10\, days The correct option is (d). It will take 10 days for 3 boys to do the same piece of work. Question 42: Find the mode of this data: 2, 0, 0, 1, 0, 3, 4, 5. Step 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. Step 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. Question 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. Question 44: From the sum 1897 and 234, subtract 2089. Step 1: Calculate the sum of 1897 and 234. 1897 + 234 = 2131 Step 2: Subtract 2089 from the sum. 2131 - 2089 = 42 The correct option is (c). The result is 42. Question 45: Bola had N4,232 and Audu had N2,834. How much did Bola have more than Audu? Step 1: Find the difference between Bola's money and Audu's money. Difference = N4232 - N2834 Step 2: Calculate the difference. Difference = N1398 The correct option is (b). Bola had N1,398 more than Audu. Question 46: What is 7½ of 400? Step 1: Convert 7½ to a decimal or improper fraction. 7(1)/(2) = 7.5 Step 2: Multiply 7.5 by 400. 7.5 × 400 = 3000 The correct option is (b). 7½ of 400 is 3000. Question 47: If 2x - 7 = 21, what is the value of x? Step 1: Add 7 to both sides of the equation. 2x - 7 + 7 = 21 + 7 2x = 28 Step 2: Divide both sides by 2. (2x)/(2) = (28)/(2) x = 14 The correct option is (d). The value of x is 14. Question 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. Question 49: Find the difference between 1000 and 418. Step 1: Subtract 418 from 1000. 1000 - 418 = 582 The correct option is (d). The difference is 582. Question 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. That's 2 down. 3 left today — send the next one.