Triangle ABC is an obtuse triangle with two congruent angles. If m< C = 108 write an expression that represents m<A
A = (180-C)/2.
To find the measure of angle A in triangle ABC, we first need to determine the measure of angle B.
Since triangle ABC is an obtuse triangle, one of the angles is greater than 90 degrees. As two angles in the triangle are congruent, the sum of these two angles must be greater than 90 degrees. Therefore, the measure of each congruent angle must be greater than 45 degrees.
The sum of the three angles in any triangle is always 180 degrees. We know that angle C has a measure of 108 degrees. Let's assume the measure of each congruent angle is x degrees.
So, the sum of the two congruent angles is 2x degrees. Adding the measure of angle C (108 degrees) to the sum of the two congruent angles will give us the sum of all three angles in triangle ABC.
2x + 108 = 180
Now, to find the value of x, we subtract 108 from both sides of the equation:
2x = 180 - 108
2x = 72
Finally, to find the measure of angle A, we substitute the value of x back into the expression:
m<A = x = 72/2 = 36 degrees
Therefore, m<A is represented by the expression 36 degrees.