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
Morning kamogelo — let's get this done. 4.1 Step 1: Identify the relationship between the angles. The angles x, 2x, and 3x lie on the straight line ABC. Angles on a straight line sum to 180^. x + 2x + 3x = 180^ (Angles on a straight line) Step 2: Combine like terms. 6x = 180^ Step 3: Solve for x. x = (180^)/(6) x = 30^ The value of x is 30^. 4.2 Step 1: Find the value of y. The lines PQ and RS are parallel. The angle y and the angle 30^ are alternate interior angles. y = 30^ (Alternate interior angles, PQ || RS) Step 2: Find the value of z. The lines PQ and RS are parallel. The angle z and the angle 42^ are alternate interior angles. z = 42^ (Alternate interior angles, PQ || RS) Step 3: Find the value of x. Consider the triangle formed by the intersection of the two transversals and the line RS. The angles in this triangle are y, x, and z. The sum of angles in a triangle is 180^. y + x + z = 180^ (Sum of angles in a triangle) Substitute the values of y and z: 30^ + x + 42^ = 180^ 72^ + x = 180^ x = 180^ - 72^ x = 108^ The sizes are: x = 108^, y = 30^, z = 42^. 4.3 Step 1: Identify the relationship between the angles. The angle c and the angle 106^ are vertically opposite angles. Vertically opposite angles are equal. c = 106^ (Vertically opposite angles) The unknown value is c = 106^. Send me the next one 📸