Answer:
∠HGB = 20°
∠ECD = 34°
∠GBH = 36°
∠FGH = 37°
Step-by-step explanation:
There are several useful rules regarding angles:
- right angles are 90°
- the sum of angles in a triangle is 180°
- angles of a linear pair are supplementary (total 180°)
- vertical angles are congruent
- an exterior angle is equal to the sum of the remote interior angles
This last observation is a consequence of the 2nd and 3rd observations.
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angle ECD
Using the last observation, ∠ECD = 124° -90° = 34°.
angle HGB
Again, using the last observation, ∠HGB = 110° -90° = 20°.
angle GBH
There are at least a couple of ways to find this one. We assume that lines FB and EC are parallel, so angles HBC and ECD are corresponding, hence congruent. Angle GBC is the supplement of of 110°, so is 70°. Then ...
∠GBH = 70° -34° = 36°
angle FGH
Again, this angle can be found multiple ways. Here, we'll use the sum of angles in triangle FGB.
∠FGB +∠GBF +∠BFG = 180°
(∠FGH +∠HGB) +∠GBF +∠BFG = 180°
∠FGH +20° +36° +87° = 180°
∠FGH = 180° -143° = 37°
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Least to greatest, the angles are ...
∠HGB = 20°
∠ECD = 34°
∠GBH = 36°
∠FGH = 37°
