In fig AB=AC NB and angle ACD= 110 find angle A
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To find angle A, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Since AB = AC, this implies that triangle ABC is an isosceles triangle, with base angles ABG and ACG being equal.
Let's start by splitting angle ACD into two equal parts. We can label the point where the angle bisector intersects AD as E.
Now, we have two angles: angle ACE and angle ECD. We know that angle ACD is 110 degrees, so angle ACE would be 110/2 = 55 degrees.
Since triangle ABC is an isosceles triangle, angle ACG is also 55 degrees. Adding all three angles in triangle ABC, we get:
angle ACE + angle ACG + angle C = 55 + 55 + C = 110 + C.
Now, we use the fact that the sum of angles in a triangle is 180 degrees:
55 + 55 + C = 180.
Combining like terms, we have:
110 + C = 180.
Subtracting 110 from both sides:
C = 180 - 110 = 70.
Now that we have the measure of angle C, we can find angle A by subtracting the sum of angles ACE and ACG from 180 degrees:
A = 180 - ACE - ACG = 180 - 55 - 55 = 70 degrees.
Therefore, angle A is 70 degrees.