Find the value of x, y, and z.

Another one kamogelo — let's solve it. 4.1 Step 1: Identify the relationship between the angles. The angles x, 2x, and 3x lie on the straight line ABC. The sum of angles on a straight line is 180^. Step 2: Set up and solve the equation for x. x + 2x + 3x = 180^ 6x = 180^ x = (180^)/(6) x = 30^ Reason: Angles on a straight line. The value of x is 30^. 4.2 Step 1: Identify parallel lines and transversals. The lines PQ and RS are parallel (indicated by the arrows). The other two lines are transversals. Step 2: Find the size of y. Angle y and the 30^ angle (at P) are alternate interior angles. Since PQ is parallel to RS, alternate interior angles are equal. y = 30^ Reason: Alternate interior angles (PQ RS). Step 3: Find the size of z. Angle z and the 42^ angle (at Q) are alternate interior angles. Since PQ is parallel to RS, alternate interior angles are equal. z = 42^ Reason: Alternate interior angles (PQ RS). Step 4: Find the size of x. Consider the triangle formed by the intersection of the two transversals and the line segment RS. The angles at R and S within this triangle are y and z. The angle vertically opposite to x is the third angle in this triangle. The sum of angles in a triangle is 180^. Let the angle at the intersection point inside the triangle be . = 180^ - (y + z) = 180^ - (30^ + 42^) = 180^ - 72^ = 108^ Angle x is vertically opposite to . Vertically opposite angles are equal. x = x = 108^ Reason: Vertically opposite angles and sum of angles in a triangle. The sizes are: x = 108^, y = 30^, z = 42^. 4.3 Step 1: Identify the relationship between the angles. The angle c and the 106^ angle are vertically opposite angles. Step 2: Determine the value of c. Vertically opposite angles are equal. c = 106^ Reason: Vertically opposite angles. The unknown angle c is 106^. Send me the next one 📸