Question

in the figure below, pentagon rstyz is a regular polygon and m∠rst = 108°. if m∠uty = 115°, what is m∠stu? a. 115° b. 137° c. 223° d. 108°

Explanation:

Step1: Recall the angle - sum property around a point

The sum of angles around a point is 360°. At point T, ∠UTY+∠STU + ∠RST=360° (since they form a complete rotation around point T).

Step2: Substitute the given values

We know that ∠RST = 108° and ∠UTY = 115°. Let ∠STU=x. Then 115°+x + 108°=360°.

Step3: Solve for x

First, simplify the left - hand side: 115°+108°+x=223°+x. Then, we have the equation 223°+x = 360°. Subtract 223° from both sides: x=360° - 223°=137°.

Answer:

B. 137°