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
1.1.1 Step 1: Determine the measure of AEC. Angles on a straight line sum to 180^. Since A, E, B form a straight line, AEC and BEC are supplementary. AEC + BEC = 180^ Given BEC = 130^: AEC + 130^ = 180^ AEC = 180^ - 130^ = 50^ Reason: Angles on a straight line. Step 2: Use the sum of angles in ACE to find x. The sum of angles in a triangle is 180^. A + ACE + AEC = 180^ Given A = x and ACE = 50^. From Step 1, AEC = 50^. x + 50^ + 50^ = 180^ x + 100^ = 180^ x = 180^ - 100^ x = 80^ Reason: Sum of angles in a triangle. The final answer is 80^. 1.1.2 Step 1: Calculate the measure of ECG using the value of x found in 1.1.1. Given ECG = 2x - 110^. Substitute x = 80^: ECG = 2(80^) - 110^ ECG = 160^ - 110^ ECG = 50^ Step 2: Compare angles to determine if AB is parallel to FG. From 1.1.1, we found AEC = 50^. We just calculated ECG = 50^. Since AEC and ECG are alternate interior angles formed by the transversal line CD intersecting lines AB and FG, and they are equal: AEC = ECG = 50^ Therefore, AB is parallel to FG. Alternatively, using co-interior angles: We have BEC = 130^ and ECG = 50^. These are co-interior angles formed by the transversal line CD intersecting lines AB and FG. BEC + ECG = 130^ + 50^ = 180^ Since the co-interior angles are supplementary, AB is parallel to FG. The final answer is Yes, AB is parallel to FG because the alternate interior angles ( AEC and ECG) are equal, or because the co-interior angles ( BEC and ECG) are supplementary.. 3 done, 2 left today. You're making progress.