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°

In the figure below pentagon RSTYZ is a regular polygon and mRST 108If mUTY 115 what is mSTUA137OB 223OC 108OD 115 class=

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ANSWER

[tex]223[/tex]

Option B

EXPLANATION

Given;

[tex]\begin{gathered} m\angle RST=108⁰. \\ m\angle UTY=115° \end{gathered}[/tex]

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

Hence;

[tex]m\angle RST=m\angle STY=108[/tex]

The measure of angle STU is;

[tex]\angle STU=\angle STY+\angle UTY[/tex]

Hence, substitute the values of the angles;

[tex]\begin{gathered} \operatorname{\angle}STU=\operatorname{\angle}STY+\operatorname{\angle}UTY \\ =108+115 \\ =223 \end{gathered}[/tex]

Therefore, the measure of angle STU is 223 degrees