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21 votes
Does anybody understand this? Been struggling with it for awhile. Use the rectangle to find the measure of the following angles. BAC=25

Does anybody understand this? Been struggling with it for awhile. Use the rectangle-example-1
User Tom Johnson
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1 Answer

14 votes
14 votes

Answer:

∠CBA =90°; ∠CAD =65°; ∠ACD =25°; ∠CBD = 65°

∠BWA = 130°; ∠AWD = 50°

Explanation:

The diagonals of a rectangle divide the figure into two pairs of congruent isosceles triangles. The figure is symmetrical about both the vertical and horizontal centerlines. Each corner angle of the rectangle is 90°. Of course, the sum of angles in any of the triangles is 180°.

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The above descriptions tell you ...

∠ABD =∠ACD =∠BAC =∠BDC = 25°

∠CBA =∠BCD =∠CDA =∠DAB = 90°

∠CAD =∠CBD =∠ACB =∠ADB = 90° -25° = 65°

∠BWA =∠CWD = 180° -25° -25° = 130°

∠AWD = ∠BWC = 180° -65° -65° = 50°

User Stefan Novak
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