Answer:
11) x = 4
12) x = 12
13) A = 45
14) A = 40
Step-by-step explanation:
All triangle angles must add up to 180 degrees. If they do not, the triangle is not considered a triangle.
So for triangle 11, solve using the equation: (16x + 4) + 47 + 65 = 180. First add 47 + 65 together to get 112. Subtract 112 from both sides to get (16x + 4) = 68. Subtract 4 from both sides to get 16x = 64. Divide 16 from both sides to get x = 4. Use the same technique for the other triangle.
For triangle 12, solve using the equation: (3x + 9) + 60 + 75 = 180. Add 60 + 75 to get 135. Subtract 135 from both sides to get (3x + 9) = 45. Subtract 9 from both sides to get 3x = 36. Divide 3 from both sides to get x = 12.
For triangle 13, solve using the equation: (62 + x) + (x + 51) + 79 = 180. For this equation, add the common variable first to get 113 + 2x + 79 = 180. You can still further simplify by adding 113 + 79 to get 192. The new equation is 192 + 2x = 180. Subtract 192 from both sides to get 2x = -12. Divide 2 from both sides to get x = -6. Now, to solve for angle A, insert the x value, -6, into Angle A's expression: x + 51. The x value would change the expression into -6 + 51. Solve to get 45. Use this technique for the other triangle as well.
For triangle 14, solve using the equation: 6x + 4x + 80 = 180. First add common variables to get 10x + 80 = 180. Subtract 80 from both sides to get 10x = 100. Divide both sides by 10 to get x = 10. To solve for Angle A, insert the x value, 10, in place of x. This turns the expression 4x into 4(10). Solve to get 40.
Hope it helps!
