This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to solve the problem using the properties of angles formed by parallel lines and a transversal. Part i: If f = 60^ and c = 8x - 4, find the value of x. Step 1: Identify the relationship between angles c and f. From the diagram, angles c and f are alternate interior angles. Since lines AB and CD are parallel (implied by the context of the problem), alternate interior angles are equal. c = f Step 2: Substitute the given values into the equation. 8x - 4 = 60^ Step 3: Solve for x. 8x = 60 + 4 8x = 64 x = (64)/(8) x = 8 Part ii: If e = 110^, find the value of a, b, c, d, f, g, and h. Step 1: Use the given angle e = 110^ to find f, g, and h at the bottom intersection. • Angles e and h are vertically opposite angles, so they are equal. h = e = 110^ • Angles e and f form a linear pair (angles on a straight line), so their sum is 180^. e + f = 180^ 110^ + f = 180^ f = 180^ - 110^ = 70^ • Angles f and g are vertically opposite angles, so they are equal. g = f = 70^ So, e = 110^, f = 70^, g = 70^, h = 110^. Step 2: Use the relationships between angles formed by parallel lines and a transversal to find a, b, c, and d at the top intersection. Since lines AB and CD are parallel: • Angles a and e are corresponding angles, so they are equal. a = e = 110^ • Angles b and f are corresponding angles, so they are equal. b = f = 70^ • Angles c and g are corresponding angles, so they are equal. c = g = 70^ • Angles d and h are corresponding angles, so they are equal. d = h = 110^ Step 3: List all the angle values. a = 110^ b = 70^ c = 70^ d = 110^ f = 70^ g = 70^ h = 110^ Send me the next one 📸