Finding $\angle ADC$ in $\triangle ABC$

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In summary, $\angle ADC$ is an angle in the triangle $\triangle ABC$ formed by the sides AC and DC. To find its measure, you can use the formula $\angle ADC = \frac{180 - (\angle BAC + \angle BCA)}{2}$ and you will need to know the lengths of at least two sides of the triangle and the measure of at least one other angle. You can also use trigonometry, specifically the law of sines or the law of cosines, to find the measure of $\angle ADC$ in certain cases such as when the triangle is a right triangle or an equilateral triangle.
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Albert1
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$\triangle ABC, \overline{AB}=\overline {AC}$,there exists an inner point ${D}$ and satisfyng :
(1)$\overline {AB}=\overline {AC}=\overline {BD}$
(2)$\angle DCB=30^o$
find $\angle ADC=?$
 
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Are these problems you need help with? Or are they just for members to try?
 
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Joppy said:
Are these problems you need help with? Or are they just for members to try?

for members to try
 
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Albert said:
$\triangle ABC, \overline{AB}=\overline {AC}$,there exists an inner point ${D}$ and satisfyng :
(1)$\overline {AB}=\overline {AC}=\overline {BD}$
(2)$\angle DCB=30^o$
find $\angle ADC=?$
my solution
explanation :
GD//BC
let DE=GH=1,
EF=FH=x,
AK=y
$\angle DEC=\angle GHB=90^o$
Triangle AGD is an equilateral triangle

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Related to Finding $\angle ADC$ in $\triangle ABC$

What is $\angle ADC$ in $\triangle ABC$?

The angle $\angle ADC$ is one of the angles in the triangle $\triangle ABC$ formed by the vertices A, B, and C. It is the angle formed by the sides AC and DC.

How do I find the measure of $\angle ADC$?

The measure of an angle is typically given in degrees, and can be found using the formula $\angle ADC = \frac{180 - (\angle BAC + \angle BCA)}{2}$. This formula applies to any triangle, including $\triangle ABC$.

What information do I need to find $\angle ADC$?

To find the measure of $\angle ADC$, you will need to know the lengths of at least two sides of the triangle and the measure of at least one other angle in the triangle. This information can be obtained through measurements, given values, or through other relevant formulas.

Can I use trigonometry to find $\angle ADC$?

Yes, you can use trigonometry to find the measure of $\angle ADC$ if you have the lengths of two sides of the triangle and the measure of one other angle. You can use the law of sines or the law of cosines to solve for the unknown angle.

Are there any special cases for finding $\angle ADC$?

Yes, there are a few special cases for finding the measure of $\angle ADC$. If the triangle is a right triangle, you can use basic trigonometry functions to find the measure of the angle. Additionally, if the triangle is an equilateral triangle, all angles will have the same measure, so $\angle ADC$ will be equal to $\frac{180}{3} = 60$ degrees.

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