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 find the values of a, b, c, and d using the properties of parallel lines. The lines CD and EF are parallel, and HI is the transversal. Step 1: Find a. Angle a and the 85^ angle are vertically opposite angles. Vertically opposite angles are equal. a = 85^ Reason: Vertically opposite angles. Step 2: Find b. Angle b and the 85^ angle form a linear pair on the straight line HI. Angles in a linear pair sum to 180^. b + 85^ = 180^ b = 180^ - 85^ b = 95^ Reason: Angles on a straight line (linear pair). Step 3: Find c. Angle c and angle b are alternate interior angles. Since lines CD and EF are parallel, alternate interior angles are equal. c = b Since b = 95^: c = 95^ Reason: Alternate interior angles are equal. Step 4: Find d. Angle d and the 85^ angle are corresponding angles. Since lines CD and EF are parallel, corresponding angles are equal. d = 85^ Reason: Corresponding angles are equal. The values are: a = 85^ b = 95^ c = 95^ d = 85^ That's 2 down. 3 left today — send the next one.