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 values of x for each diagram: 1. Top Left Diagram Step 1: Identify the relationship between the angles. The angles 60^ and x form a right angle. Reason: Angles in a right angle sum to 90^. Step 2: Set up the equation and solve for x. 60^ + x = 90^ x = 90^ - 60^ x = 30^ 1. Top Right Diagram Step 1: Identify the relationship between the angles. The angles 30^, 80^, and 2x lie on a straight line. Reason: Angles on a straight line sum to 180^. Step 2: Set up the equation and solve for x. 30^ + 80^ + 2x = 180^ 110^ + 2x = 180^ 2x = 180^ - 110^ 2x = 70^ x = (70^)/(2) x = 35^ 2. Middle Left Diagram Step 1: Identify the relationship between the angles. The angles 2x and 26^ form a right angle. Reason: Angles in a right angle sum to 90^. Step 2: Set up the equation and solve for x. 2x + 26^ = 90^ 2x = 90^ - 26^ 2x = 64^ x = (64^)/(2) x = 32^ 2. Middle Right Diagram Step 1: Identify the relationship between the angles. Assuming the horizontal line is a straight line, the angles x and 150^ are supplementary. Reason: Angles on a straight line sum to 180^. Step 2: Set up the equation and solve for x. x + 150^ = 180^ x = 180^ - 150^ x = 30^ 3. Bottom Left Diagram Step 1: Identify the relationship between the angles. The angles 22^, x, and 77^ are the interior angles of a triangle. Reason: Angles in a triangle sum to 180^. Step 2: Set up the equation and solve for x. 22^ + x + 77^ = 180^ x + 99^ = 180^ x = 180^ - 99^ x = 81^ 3. Bottom Right Diagram Step 1: Identify the relationship between the angles. The angles (x)/(2) and 74^ are adjacent angles on a straight line. Reason: Angles on a straight line sum to 180^. Step 2: Set up the equation and solve for x. (x)/(2) + 74^ = 180^ (x)/(2) = 180^ - 74^ (x)/(2) = 106^ x = 106^ × 2 x = 212^ Last Problem (Bottom Diagram) Step 1: Identify the relationship between the angles. The three angles, each marked as x, lie on a straight line. Reason: Angles on a straight line sum to 180^. Step 2: Set up the equation and solve for x. x + x + x = 180^ 3x = 180^ x = (180^)/(3) x = 60^ That's 2 down. 3 left today — send the next one.