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In ABC, let point D lie on the side AB, and point E lie on the side BC, such that m BDC = 60 degrees, and m AEC = 120 degrees. Find the measure of BCD if m BAE = 21 degrees.

TYSM :)

Mar 23, 2021

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Hello

Can you somehow post a picture of the problem (show the angles all drawn out) so that I can get a better idea of what I am trying to solve?

The Math Whiz

Mar 23, 2021
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Here is a drawing I attempted to make. Hope this helps!

HelpPls123abc  Mar 23, 2021
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Thank you so much! Let my try to work out the problem now!

TheMathWhiz  Mar 23, 2021
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Hello again! This is my answer to the problem:

We know that the sum of interior angles in a triangle is 180 degrees. So the triangle made up of C, E, and the final, unlabled point (I am going to call this Y), must have this sum. This means that BCD must be less than 180-120=60 degrees.

I can find angle CDA, 180 (the number of degrees in a line) - 60 (the number of degrees we already know are on the line), which gives us 120.

Using this data, 180-(120+21 [the sum of the angles we alread know in the DYA triangle])=39 degrees, the number of degrees that are in angle AYD.

Because the angles are symmetric, angle CYE is also 39 degrees.

To finish this problem off, BCD is the same as ECD. When we know that two angles are 39 and 120, the final answer is that ECD/BCD is 180-(39+120) = 21 degrees.

To check, 21<60, so our answer does work!

BCD is 21 degrees.

Thank you so much for making an image, this really helped me solve the problem! I hope this helped!

The Math Whiz

Mar 23, 2021
edited by TheMathWhiz  Mar 23, 2021
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Sorry it took me so long to type up my answer, it was a fun problem, I enjoyed solving it! ðŸ˜€ðŸ˜‹ðŸ˜‰

TheMathWhiz  Mar 23, 2021