Answer
PART 1
Option C is correct.
x = 7°
PART 2
Option A is correct.
Angle A = 157°
Explanation
Vertical angles are angles that are directly opposite each other at a point where two straight lines intersect. Vertical angles are equal to each other.
Since vertical angles are equal, we can equate (x + 16)° and (4x - 5)° in order to solve for x
(x + 16)° = (4x - 5)°
x° + 16° = 4x° - 5°
x° - 4x° = -5° - 16°
-3x° = -21°
Divide both sides by -3
(-3x°/-3) = )-21°/-3)
x° = 7°
For the second part, we need to note that the sum of angles on a straight line is 180°.
So,
(x + 16°) + Angle A = 180°
x° + 16° + Angle A = 180°
x° = 7°
x° + 16° + Angle A = 180°
7° + 16° + Angle A = 180°
23° + Angle A = 180°
Angle A = 180° - 23°
Angle A = 157°
Hope this Helps!!!
