angle computational (2017 Zhautykov City VII P2)

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angle computational (2017 Zhautykov City VII P2)

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#1 h Aug 16, 2019, 8:52 PM • 2 Y

Y by Adventure10, Mango247

The triangle is $ABC$ . The point $K$ is taken on the side $AB$ , and the point $L$ is taken on the side $AC$ so that $\angle ACB + \angle AKL = 50 {}^\circ$ and $\angle ABC + \angle ALK = 70 {}^\circ$ . What could be the angle $\angle BAC$ ?

This post has been edited 1 time. Last edited by parmenides51, Dec 19, 2022, 12:04 PM

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#2 h Aug 16, 2019, 9:41 PM • 1 Y

Y by Adventure10

We're trying to find $m\angle BAC$ , so we can let $x = m\angle BAC$ . Also, let $a = m\angle AKL$ . From here, try to find the measures of all the other angles in the problem in terms of $x$ and $a$ using the given information, and see if you can use relationships among the angles to solve for $x$ .
Solution
(Check to make sure that makes sense, in case I made a mistake.)

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