Final answer:
To find the measure of each acute angle, set up an equation and solve for x. Substituting the value of x, the measure of each acute angle is 55° and 35°.
Step-by-step explanation:
To find the measure of each acute angle, we need to set up an equation and solve for x.
The equation is: (6x + 7)° + (2x + 19)° = 90°.
Simplifying the equation, we get: 8x + 26 = 90.
Subtracting 26 from both sides, we have: 8x = 64.
Finally, dividing both sides by 8, we get: x = 8.
Substituting x back into the expressions for the angles, we find: (6(8) + 7)° = 55° and (2(8) + 19)° = 35°.
Therefore, the measure of each acute angle is 55° and 35°.