9514 1404 393
Answer:
- ∠a = 133°
- ∠b = 15°
- ∠c = 75°
- ∠d = 58°
Step-by-step explanation:
We don't know the definitions, properties, postulates, or theorems on your list, so we'll use the following:
- a right angle measures 90°
- a straight angle measures 180°
- the acute angles in a right triangle total 90°
- an exterior angle of a triangle is equal to the sum of the remote interior angles
- the measure of an angle is equal to the sum of the measures of its parts.
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∠a = 180° -47° = 133°; reasons 2, 5. The angles form a straight angle.
∠b = 47° -32° = 15°; reason 4
∠c = 90° - ∠b = 90° -15° = 75°; reason 3
∠d = 90° -32° = 58°; reasons 1, 5. The angles form a right angle. If you want to get picky, we know it is a right angle by reasons 1 and 2. The marked right angle and the sum of 32° and ∠d together form a straight angle.
