Answer
$20^{\circ},35^{\circ}, 125^{\circ},55^{\circ}$
Work Step by Step
1. Given 2 interior angles and 1 exterior angle of the triangle. We can use exterior angle to find the third interior angle of the triangle. We just need to subtract the exterior angle from 180 degrees.
$180^{\circ}-(7-12x)^{\circ}=12x+173$
2. The sum of interior angles of the triangle equal to the 180 degrees
$(-5x)^{\circ}+(-8x+3)^{\circ}+(12x+173) ^{\circ}=180^{\circ}$
3. Solve the equation for x:
$-x+176=180$
$x=-4^{\circ}$
4. Then find all the interior angles by replacing x=-4:
$-5(-4)=20^{\circ}$
$-8(-4)+3=35^{\circ}$
$12(-4)+173=125^{\circ}$
5. Then find the exterior angle:
$7-12(-4)=55 ^{\circ}$
It is not a coincidence that the sum of 2 interior angles equal to the exterior angle.
