In the figure below, pentagon RSTYZ is a regular polygon and m/RST = 108⁰.If m/UTY = 115°, what is m/STU?A137°OB. 223°OC. 108°OD. 115°

Question

asked Dec 10, 2023 113k views

1 Answer

Anil Chaudhari · Answer 1 · 2023-12-15T07:31:31+0000

ANSWER

Option B

Step-by-step explanation

Given;

$\begin{gathered} m\angle RST=108⁰. \\ m\angle UTY=115° \end{gathered}$

Note that the pentagon is a regular polygon (all the angles are equal).

Hence;

$m\angle RST=m\angle STY=108$

The measure of angle STU is;

$\angle STU=\angle STY+\angle UTY$

Hence, substitute the values of the angles;

$\begin{gathered} \operatorname{\angle}STU=\operatorname{\angle}STY+\operatorname{\angle}UTY \\ =108+115 \\ =223 \end{gathered}$

Therefore, the measure of angle STU is 223 degrees