Answer: ∠A = 44°Step-by-step explanation:Let b represent the measure of the exterior angle at B. Let c represent the measure of the exterior angle at C. The sum of angles in the lower triangle is ... b/2 +c/2 +68° = 180° b +c = 360° -136° . . . . . multiply by 2, subtract 136° b +c = 224°__The exterior angle b is the supplement of the interior angle there, so the interior angle B is ... B = 180° -bThe exterior angle c is the sum of the remote interior angles, so we have ... c = B +A c = (180° -b) +A A = (b +c) -180° . . . . . . . . add b-180° to both sides A = 224° -180° = 44° . . . . substitute for (b+c)The measure of angle A is 44°._____Additional commentThe angle naming is perhaps a little unconventional, but we wanted to use names that made the answer less cumbersome to write. We consider the angle A, B, C to be the interior angles of ΔABC, and we have named the exterior angles at B and C as 'b' and 'c'. Conventionally, 'b' and 'c' would name the sides opposite angles B and C, respectively. We're not concerned with side lengths here, so we used those letters for an unconventional purpose.