Final answer:
The measure of angle 1 (m/1) is 35 degrees, which is found by solving the equation formed by adding the measures of angles 1 and 2 (2x + 7 and 3x + 13) and setting them equal to 90 degrees because they are complementary angles formed by an altitude.
Step-by-step explanation:
The student is given that EC is an altitude of triangle AED, with the measure of angle 1 (m/1) being 2x + 7, and the measure of angle 2 (m/2) equaling 3x + 13. Since EC is an altitude, it implies that it is perpendicular to AD and creates a right angle at E. Hence, angles 1 and 2 are complementary and together make 90 degrees. By setting up the equation 2x + 7 + 3x +13 = 90, we can solve for x and then find m/1.
Solving the equation, we get 5x + 20 = 90. Subtract 20 from both sides to get 5x = 70. Dividing both sides by 5, we find x = 14. Substituting x back into the expression for m/1, we get m/1 = 2(14) + 7 = 28 + 7 = 35 degrees. Therefore, the measure of angle 1 is 35 degrees.