Please help me- Find the angles:
m∠A = 2/3x°
m∠P = 4/5x°
∠A and ∠P are supplementary.

9514 1404 393

  m∠A = 81 9/11°

  m∠P = 98 2/11°

Step-by-step explanation:

Supplementary angles have a total of 180°, so we have ...

  m∠A +m∠P = 180°

  2/3x° +4/5x° = 180°

  22/15x° = 180°

  x = 122 8/11 . . . . . . multiply by 15/22

Then the angles are ...

  m∠A = (2/3)(122 8/11)°

  m∠A = 81 9/11°

  m∠P = (4/5)(122 8/11)°

  m∠P = 98 2/11°

Alternate solution

The fraction of 180° that is ∠A is ...

  (2/3x°)/(2/3x° +4/5x°) = (10/15)/(10/15 +12/15) = 10/22 = 5/11

  m∠A = (5/11)(180°) = 81 9/11°

  m∠P = 180° -m∠A = 98 2/11°

m∡A = 81.8°

m∡P = 98.2°

Step-by-step explanation:

2/3x + 4/5x = 180

multiply each side by 15 to eliminate fractions

10x + 12x = 2700

22x = 2700

x = 122.7

∡A = 2/3 (122.7) = 81.8

∡P = 4/5 (122.7) = 98.2