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Can anyone help? can’t figure this one out

Can anyone help? can’t figure this one out-example-1
User Cffk
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1 Answer

7 votes

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°

Can anyone help? can’t figure this one out-example-1
User Anton Harniakou
by
7.8k points