Respuesta :

mhanifa

Answer:

  • x > 6
  • 6 < x < 62

Step-by-step explanation:

Question 5

The sides containing the given angles 37 and 84 are of same length:

one side is marked same, the second side is common.

The sides opposite angles of 37 and 84 are proportional to those angles, therefore:

  • 0< x + 14 < 2(3x - 8)

The first part:

  • x > - 14

The second part:

  • x + 14 < 6x - 16
  • 5x > 30
  • x > 6

Combination of the two is:

  • x > 6

Question 6

The triangles are isosceles, because:

  • The left triangle has two equal angles, so the opposite sides are congruent
  • The common side with the right triangle is same as marked side, so the triangle on the right is also isosceles.

The angles between equal sides

Left triangle:

  • 180° - 2*70° = 40°

Right triangle:

  • 180° - 2*66° = 48°

Since 40° < 48°, the opposite sides will have same inequality due to being proportional to angles:

  • 3x - 18 < 2(x + 22)
  • 3x - 18 < 2x + 44
  • 3x - 2x < 44 + 18
  • x < 62

Same time we know the side must be a positive number:

  • 3x - 18 > 0
  • 3x > 18
  • x > 6

So the possible values of x are:

  • 6 < x < 62 or x = (6, 62)

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