Answer:
a) x = 45°
b) yes, the sides are parallel (ABCD is a trapezoid)
Step-by-step explanation:
(a)
The relevant relation is the sum of angles in a quadrilateral is 360°.
2x +3x +x +90 = 360
6x = 270 . . . . . . collect terms, subtract 90
x = 270/6 = 45
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(b)
Then the angle at A is ...
∠A = 2x° = 2(45)° = 90°
The sum of the angles at A and D is 180°, so the converse of the consecutive interior angles theorem applies. It means segments AD and BC are parallel.
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Additional comment
The consecutive interior angles theorem says that when a transversal crosses parallel lines, consecutive interior angles are supplementary.
