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 the marked angles: Step 1: Solve for angle f in Figure 1. The angles 72^, 56^, and f are the interior angles of the top triangle. The sum of angles in a triangle is 180^. 72^ + 56^ + f = 180^ 128^ + f = 180^ f = 180^ - 128^ f = 52^ The value of f is 52^. Step 2: Solve for angles y and z in Figure 2. Angle z and the exterior angle 107^ are angles on a straight line, so their sum is 180^. z + 107^ = 180^ z = 180^ - 107^ z = 73^ Now, use the sum of angles in the triangle: y + 50^ + z = 180^. y + 50^ + 73^ = 180^ y + 123^ = 180^ y = 180^ - 123^ y = 57^ The values are y = 57^ and z = 73^. Step 3: Solve for angles a and x in Figure 3. The interior angle 4x and the exterior angle 5x are angles on a straight line, so their sum is 180^. 4x + 5x = 180^ 9x = 180^ x = (180^)/(9) x = 20^ Now, use the sum of angles in the triangle: a + 3x + 4x = 180^. a + 3(20^) + 4(20^) = 180^ a + 60^ + 80^ = 180^ a + 140^ = 180^ a = 180^ - 140^ a = 40^ The values are x = 20^ and a = 40^. Step 4: Solve for angle c in Figure 4. The interior angle adjacent to the exterior angle 120^ is 180^ - 120^ = 60^. Now, use the sum of angles in the triangle: c + 39^ + 60^ = 180^. c + 99^ = 180^ c = 180^ - 99^ c = 81^ The value of c is 81^. Step 5: Solve for angles d and e in Figure 5. In the top triangle, the sum of angles is 180^. e + 50^ + 38^ = 180^ e + 88^ = 180^ e = 180^ - 88^ e = 92^ Angle d is vertically opposite to the 38^ angle in the top triangle, or we can use the sum of angles in the bottom triangle. The interior angle adjacent to the exterior angle 130^ is 180^ - 130^ = 50^. In the bottom triangle, the angles are d, e (which is 92^), and 50^. d + 92^ + 50^ = 180^ d + 142^ = 180^ d = 180^ - 142^ d = 38^ The values are d = 38^ and e = 92^. Step 6: Solve for angle g in Figure 6. This is a right-angled triangle, so one angle is 90^. The sum of angles in a triangle is 180^. g + 90^ + 47^ = 180^ g + 137^ = 180^ g = 180^ - 137^ g = 43^ The value of g is 43^. What's next? Send 'em! 📸