Triangle Angles

Here are the solutions to the problems: 5. Triangle Angles A triangle has angles in the ratio 2:3:4. What is the measure of the largest angle? Step 1: Find the sum of the ratio parts. Sum of ratio parts = 2 + 3 + 4 = 9 Step 2: The sum of angles in a triangle is 180^. Divide this by the sum of the ratio parts to find the value of one part. Value of one part = (180^)/(9) = 20^ Step 3: The largest ratio part is 4. Multiply this by the value of one part to find the largest angle. Largest angle = 4 × 20^ = 80^ The measure of the largest angle is 80^. 6. LCM and GCD Product Find the product of the L.C.M and G.C.D of 10, 20 and 40. Step 1: Find the prime factorization of each number. 10 = 2 × 5 20 = 2^2 × 5 40 = 2^3 × 5 Step 2: Determine the G.C.D (Greatest Common Divisor). This is the product of the lowest powers of common prime factors. G.C.D(10, 20, 40) = 2^1 × 5^1 = 10 Step 3: Determine the L.C.M (Least Common Multiple). This is the product of the highest powers of all prime factors present. L.C.M(10, 20, 40) = 2^3 × 5^1 = 8 × 5 = 40 Step 4: Find the product of the L.C.M and G.C.D. Product = L.C.M × G.C.D = 40 × 10 = 400 The product of the L.C.M and G.C.D is 400. 7. Prime Factorization Write 2700 and 750 as product of their prime factors. For 2700: Step 1: Divide 2700 by the smallest prime factors. 2700 = 100 × 27 = (10^2) × (3^3) 2700 = (2 × 5)^2 × 3^3 2700 = 2^2 × 5^2 × 3^3 The prime factorization of 2700 is 2^2 × 3^3 × 5^2. For 750: Step 1: Divide 750 by the smallest prime factors. 750 = 10 × 75 = (2 × 5) × (3 × 25) 750 = 2 × 5 × 3 × 5^2 750 = 2 × 3 × 5^3 The prime factorization of 750 is 2 × 3 × 5^3. 8. Hire Purchase Calculation Samson was offered to purchase a mobile phone whose cash price is 50000 at hire purchase which included a deposit of 20% of the cash price followed by 12 equal monthly installments of 4000 each. Calculate how much more did Samson pay for the phone. Step 1: Calculate the deposit amount. Deposit = 20\% of 50000 = 0.20 × 50000 = 10000 Step 2: Calculate the total amount paid in installments. Total installments = 12 months × 4000/month = 48000 Step 3: Calculate the total hire purchase price. Hire purchase price = Deposit + Total installments = 10000 + 48000 = 58000 Step 4: Calculate how much more Samson paid compared to the cash price. Extra paid = Hire purchase price - Cash price = 58000 - 50000 = 8000 Samson paid 8000 more for the phone. 9. Equation of a Line The equation of a line is 4y - 16x - 20 = 0. a) Find the gradient of the line. Step 1: Rearrange the equation into the slope-intercept form (y = mx + c). 4y - 16x - 20 = 0 4y = 16x + 20 Step 2: Divide the entire equation by 4. y = (16x)/(4) + (20)/(4) y = 4x + 5 Step 3: Identify the gradient (m), which is the coefficient of x. The gradient of the line is 4. b) Find the value of x at a point when y = -11. Step 1: Substitute y = -11 into the original equation 4y - 16x - 20 = 0. 4(-11) - 16x - 20 = 0 Step 2: Simplify and solve for x. -44 - 16x - 20 = 0 -64 - 16x = 0 -16x = 64 x = (64)/(-16) x = -4 The value of x when y = -11 is -4. That's 2 down. 3 left today — send the next one.