Calculate Angle A in a Quadrilateral with Parallel Sides and Diagonals

ABCD is a quadrilateral.

AB||CD
AC||BD

Calculate angle A ∢A .

90°90°90°AAABBBDDDCCC45°45°

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find angle A
00:05 The sum of angles in a triangle is always equal to 180
00:14 Let's substitute appropriate values according to the given data
00:29 and isolate A
00:48 and this is the solution to the problem

Step-by-step written solution

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1

Understand the problem

ABCD is a quadrilateral.

AB||CD
AC||BD

Calculate angle A ∢A .

90°90°90°AAABBBDDDCCC45°45°

2

Step-by-step solution

Angles ABC and DCB are alternate angles and equal to 45.

Angles ACB and DBC are alternate angles and equal to 45.

That is, angles B and C together equal 90 degrees.

Now we can calculate angle A, since we know that the sum of the angles of a square is 360:

360909090=90 360-90-90-90=90

3

Final Answer

90°

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Indicates which angle is greater

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