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
a) Angles on a straight line sum to 180^. These are supplementary angles or angles on a straight line. Step 1: Set up the equation for the sum of angles on a straight line. A + B + C = 180^ Step 2: Substitute the given values A = 55^ and B = 75^. 55^ + 75^ + C = 180^ Step 3: Solve for C. 130^ + C = 180^ C = 180^ - 130^ C = 50^ The size of C is 50^. b) The sum of angles in a triangle is 180^. These are angles in a triangle. Step 1: Set up the equation for the sum of angles in a triangle. A + B + C = 180^ Step 2: Substitute the given values A = 90^ and B = 35^. 90^ + 35^ + C = 180^ Step 3: Solve for C. 125^ + C = 180^ C = 180^ - 125^ C = 55^ The size of C is 55^. c) The sum of angles in a quadrilateral is 360^. These are angles in a quadrilateral. Step 1: Set up the equation for the sum of angles in a quadrilateral. A + B + C + D = 360^ Step 2: Substitute the given values A = 150^, B = 30^, and C = 150^. 150^ + 30^ + 150^ + D = 360^ Step 3: Solve for D. 330^ + D = 360^ D = 360^ - 330^ D = 30^ The size of D is 30^. That's 2 down. 3 left today — send the next one.