Final answer:
To find the measure of angle STU, first solve the equations for W. Then, use the values of W to find the angles M∠RTU and M∠STU. The measure of angle STU is 69°.
Step-by-step explanation:
To find the measure of angle STU, we first need to determine the value of W. Since RS = RU, we can equate their corresponding angle measures: M∠RTS = M∠RTU. Setting up the equation: 5W - 69° = W + 3°.
Simplifying the equation, we get 4W = 72°. Dividing both sides by 4, we find W = 18°.
Now that we know the value of W, we can substitute it into the equation M∠RTU = W + 3°: M∠RTU = 18° + 3° = 21°.
Finally, to find the measure of angle STU, we know that the sum of the angles in a triangle is 180°. Therefore, M∠STU = 180° - M∠RTS - M∠RTU = 180° - (5W - 69°) - (W + 3°).
Substituting the values, we get M∠STU = 180° - (5(18°) - 69°) - (18° + 3°) = 180° - 90° - 21° = 69°.