t = 7
Given the acute angle, m < 49°, and the right angle with a measure of 90°, and the angle with a measure of m < (5t + 6)°:
Since their sum add up to 180°, we can establish the following formula:
180° = (5t + 6)° + 90° + 49°
180° = 5t + 6 + 139°
180° = 5t + 145°
Subtract 145° from both sides:
180° - 145° = 5t + 145° - 145°
35° = 5t
Divide both sides by 5 to solve for t:
35°/5 = 5t/5
7° = t
Therefore, the value of t = 7°.
Verify whether we derived the correct answer by plugging in t = 7° into the equation:
180° = (5t + 6)° + 90° + 49°
180° = (5(7) + 6)° + 90° + 49°
180° = (35 + 6)° + 90° + 49°
180° = (41)° + 90° + 49°
180° = (41)° + 90° + 49°
180° = 180°
Therefore, t = 7° is the correct answer.