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Basic geometry: angle calculation. #16

Open Ams627 opened 1 year ago

Ams627 commented 1 year ago

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Ams627 commented 1 year ago

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The pentagon ABCDE consists of an isosceles, equilateral and right-angled triangle. The base of the isosceles triangle is side AB. Sides BC and AE of the pentagon are parallel.

What is the size of the angle 𝜔? Do not measure the sizes of the angles, but calculate them!.

Solution

Extend line AB to point P as shown:

image

Due to AE and BC being parallel, angle CBP is also 55 degrees. Due to BED being an equilateral triangle, angle DBE is 60 degrees. Due to triangle ABE being isoceles, angle ABE is 55 degrees. therefore angle CBD is 180 - 60 - 55 - 55. So angle CBD is 10 degrees and 𝜔 is 80 degrees.

Ams627 commented 1 year ago

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