Answer:
Please check the explanation.
Explanation:
We know that a pentagon is a polygon with 5 sides and 5 angles.
Given the polygon with 5 angles.
A pentagon is a polygon with 5 sides and 5 angles.
The angles of the given pentagon are:
∠P = (4x + 2)°
∠Q = 132°
∠R = (4x - 10)°
∠S = (5x - 11)°
∠T = 128°
We know that the sum of the measures of the interior angles of a pentagon is 540 degrees.
Therefore,
∠P + ∠Q + ∠R + ∠S + ∠T = 540°
(4x + 2)° + 132° + (4x - 10)° + (5x - 11)° + 128° = 540°
group similar elements
4x + 4x + 5x + 2 + 132 - 10 - 11 + 128 = 540
simplify
13x + 241 = 540
subtract 241 from both sides
13x + 241 - 241 = 540 - 241
13x = 299
divide both sides by 13
13x/13 = 299/13
x = 23
Thus, the value of x = 23
Therefore, the measure of angle ∠S is:
m∠S = (5x - 11)°
= (5(23) - 11)°
= (115 - 11)°
= 104°
Thus,
m∠S = 104°