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 are the solutions for the given problems. Problem 1: a) Find x and y for the top triangle. Step 1: Find the value of y. The sum of the interior angles in a triangle is 180^. 60^ + 80^ + y = 180^ 140^ + y = 180^ y = 180^ - 140^ y = 40^ Step 2: Find the value of x. The angle x is an exterior angle of the triangle. An exterior angle is equal to the sum of the two opposite interior angles. x = 60^ + 80^ x = 140^ Alternatively, x and y form a linear pair, so x + y = 180^. x + 40^ = 180^ x = 180^ - 40^ x = 140^ The values are: x = 140^ y = 40^ Problem 2: b) Find x and y for the bottom triangle. Step 1: Find the value of y. The square symbol indicates a right angle, which is 90^. The sum of the interior angles in a triangle is 180^. 41^ + 90^ + y = 180^ 131^ + y = 180^ y = 180^ - 131^ y = 49^ Step 2: Find the value of x. The angle x is an exterior angle of the triangle. An exterior angle is equal to the sum of the two opposite interior angles. x = 41^ + 90^ x = 131^ Alternatively, x and y form a linear pair, so x + y = 180^. x + 49^ = 180^ x = 180^ - 49^ x = 131^ The values are: x = 131^ y = 49^