Answer:
d = 47°
Explanation:
Image is attached
Sum of angles drawn along a straight line = 180°:
The angle drawn in pink : 180° - 112° = 68°
The angle drawn in green: 180° - 66° = 114°
The angle drawn in yellowish orange: 180° - 23° = 157°
The angle marked in purple: 180° - 102° = 78°
The figure drawn in the center is a 5-sided irregular pentagon
∴ Sum of interior angles in a 5-sided polygon = (n - 2) ×180°
= (5 - 2) × 180°
= 540°
The four angles calculated above will assist in calculating the fifth remaining angle of the pentagon (which is marked in light blue):
68° + 114° + 78° + 157° + angle in light blue = 540°
Angle in light blue = 540° - 68° - 114° - 78° - 157°
= 123°
Sum of angles drawn along a straight line = 180°:
Angle marked in dark blue = 180° - 123°
= 57°
Now focus on the angles present inside the triangle
Sum of interior angles of a triangle = 180°
= d + 76° + 57° = 180°
d has to be isolated and made the subject of the equation:
d = 180° - 76° - 57°
d = 47°