In triangle ABC, the outer angle at vertices B and C is 105 and 145, respectively.

In triangle ABC, the outer angle at vertices B and C is 105 and 145, respectively. Find the degree measure of angle A.

This problem can be solved in two ways, consider one of them:

First, find the angles B and C. The sum of adjacent angles is 180 °, therefore:
B = 180 ° – 105 ° = 75 °;
C = 180 ° – 145 ° = 35 °.

Now that we know these angles, we can find the angle A, following from the fact that the sum of all angles in a triangle is 180 °:
A = 180 ° – (B + C) = 180 ° – (75 ° + 35 °) = 180 ° – 110 ° = 70 °.

Answer: 70 °.