9514 1404 393
Answer:
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°
