SOLUTION: in the accompanying diagram of Triangle ABC, AB is congruent to AC. The measure of Angle B is 40 degrees. What is the measure of Angle A?

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Question 552045: in the accompanying diagram of Triangle ABC, AB is congruent to AC. The measure of Angle B is 40 degrees. What is the measure of Angle A?
Found 2 solutions by KMST, AnlytcPhil:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
A triangle ABC with sides AB and AC that are congruent is an isosceles triangle. The angles opposite the congruent sides (angle C and angle B) are congruent.
Since the sum of the measures of the angles of a triangle is 180 degrees, and angles B and C measure 40 degrees each, the measure of angle A (in degrees) is
180-40-40=100.

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
 

Since AB is congruent to AC, we know that ᐃABC is
isosceles.  Therefore we know that its base angles are
congruent and thus have the same measure.  Therefore we
will label the measure of the other base angle C, m∠A = 40°
as well:
 

Since we know that the sum of the measures of the three angles of any 
triangle must always equal to 180°, we can write

m∠A + m∠B + m∠C = 180°

m∠A + 40° + 40° = 180°

      m∠A + 80° = 180°

            m∠A = 180° - 80°

            m∠A = 100°



Edwin