Question

If the measurement of angle RSU equals 5X + 7° and the measurement of angle UST equals 9X - 1°. If the angle of RSU and the angle of UST are complementary, find the measure of each angle.

Answer 1

The measure of angle RSU is 37° and the measure of angle UST is 53°.

Step-by-step explanation:

To find the measure of each angle, we need to set up an equation using the fact that the angles are complementary.

Since the angle of RSU and UST are complementary, we have:

5X + 7° + 9X - 1° = 90°

Combining like terms, we get:

14X + 6° = 90°

Subtracting 6° from both sides:

14X = 84°

Dividing both sides by 14:

X = 6°

Now we can find the measure of angle RSU and UST:

Angle RSU = 5X + 7°

= 5(6°) + 7°

= 30° + 7°

= 37°

Angle UST = 9X - 1°

= 9(6°) - 1°

= 54° - 1°

= 53°