Answer:
[tex] m\angle 1 = 22\degree [/tex]
[tex] m\angle 2 = 68\degree [/tex]
Step-by-step explanation:
[tex] \sin(x + 7) = \cos(4x + 8) \\ \sin(x + 7) = \sin \{90 - (4x + 8) \} \\ \{ \because \cos \theta = \sin(90 \degree - \theta) \}\\ \therefore \: (x + 7) = 90 - (4x + 8) \\ x + 7 + 4x + 8 = 90 \\ 5x = 90 - 15 \\ 5x = 75 \\ x = \frac{75}{5} \\ x = 15[/tex]
(x + 7)° = (15 + 7)° = 22°
(4x + 8)° = (4*15 + 8)° = (60 + 8)° = 68°
[tex] m\angle 1 = 22\degree [/tex]
[tex] m\angle 2 = 68\degree [/tex]
