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
Let's solve the problems step by step. Question 4 a) Find the size of angles \( x \), \( y \), and \( z \). The diagram shows a cyclic quadrilateral. The opposite angles of a cyclic quadrilateral sum to \(180^\). Step 1: Find angle \( x \). The angles \( x \) and \( 68^ \) are opposite angles in the cyclic quadrilateral. x + 68^ = 180^ x = 180^ - 68^ x = 112^ The size of angle \( x \) is \(112^\). Step 2: Find angle \( y \). The angles \( y \) and \( 38^ \) are opposite angles in the cyclic quadrilateral. y + 38^ = 180^ y = 180^ - 38^ y = 142^ The size of angle \( y \) is \(142^\). Step 3: Find angle \( z \). The angles \( z \) and \( 55^ \) are opposite angles in the cyclic quadrilateral. z + 55^ = 180^ z = 180^ - 55^ z = 125^ The size of angle \( z \) is \(125^\). b) Find the size of angle \( z \). The diagram shows a circle with center \( O \), and \( RS \) is a diameter. Step 1: Recognize that \( RUS \) is a right angle because it subtends the diameter \( RS \). RUS = 90^ Step 2: Use the angles in triangle \( RUS \). The sum of angles in a triangle is \( 180^ \). RUS + 50^ + 45^ = 180^ 90^ + 50^ + 45^ = 180^ Step 3: Solve for angle \( z \). Since \( RUS = 90^ \), the angle \( z \) is the remaining angle in the triangle. z = 180^ - 90^ - 50^ z = 40^ The size of angle \( z \) is \(40^\). 3 done, 2 left today. You're making progress.