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I did A months ago and have completely forgotten how to do this, can anyone help?

I did A months ago and have completely forgotten how to do this, can anyone help?-example-1
User Mgonto
by
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1 Answer

4 votes

Answer:

a) x = 45°

b) yes, the sides are parallel (ABCD is a trapezoid)

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.

_____

Additional comment

The consecutive interior angles theorem says that when a transversal crosses parallel lines, consecutive interior angles are supplementary.

User John R
by
6.6k points
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