a = 85°
Step-by-step explanation:
Method 1
5x = 2x + 57° (An exterior angle of a triangle is equal to the sum of its two interior opposite angles)
3x = 57°
x = 57/3 = 19°
a = 180 - 57 - 2x
a = 180 - 57 -2(19)
a = 85°
Method 2
2x + a + 57° = 180°
2x + a = 123° ==> 1
5x + a = 180°
x = (180° - a)/5 ==> 2
By substitution
2((180° - a)/5) + a = 123°
(360° - 2a)/5 + a = 123°
(360° - 2a)/5 = 123° - a
360° - 2a = 5(123° - a)
360° - 2a = 615° - 5a
-2a + 5a = 615° - 360°
3a = 255°
a = 85°
