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Angles LMN and OMP have the following measures:

m∠LMN = (x + 16)°, m∠OMP = (2x − 13)°.

Part A: If angle LMN and angle OMP are complementary angles, find the value of x. Show every step of your work. (4 points)

Part B: Use the value of x from Part A to find the measures of angles LMN and OMP. Show every step of your work. (4 points)

Part C: Could the angles also be vertical angles? Explain. (4 points)

Respuesta :

mhanifa

Given

  • Angles LMN and OMP,
  • m∠LMN = (x + 16)°,
  • m∠OMP = (2x − 13)°

Part A

If the two angles are complementary, they sum to 90°.

Set this as equation and solve for x:

  • x + 16 = 2x - 13
  • 2x - x = 16 + 13
  • x = 29

Part B

Find the measures of the two angles by substituting the value of x:

  • m∠LMN =  (29 + 16)° = 45°
  • m∠OMP = (2*29 - 13)° = 45°

Part C

These are equally sized angles but can't be vertical, because:

  • Vertical angles are formed by two intersecting lines and share same vertex. The given angles have no common point, therefore not vertical angles.

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