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Every day at 8 AM, new videos are updated and released on time for free learning. Below is a problem that everyone can think about and calculate independently on their draft paper.There is a detailed video explanation at the end of the article.
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Now, let’s take a look at this problem together. As shown in the figure, the angle bisector BD of angle ABC intersects the external angle of triangle ACB at point D. Connect AD. If ∠BDC = 40°, how do we find the measure of ∠DAC?
This problem is somewhat similar to the previous one, where we have an angle bisector of a triangle intersecting with the bisector of an external angle. We should immediately think of the conclusion from the previous problem, ∠BDC = 1/2 ∠BAC, thus ∠BAC = 80°.
Now we need to find the measure of ∠DAC, what should we do?
When we see the angle bisector, we should immediately think of the most commonly used auxiliary line related to intersection and angle bisectors, which is to draw perpendiculars to both sides of the angle. For a detailed analysis of the process, please see the video below.
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