A quadrilateral is a polygon with 4 number of sides and 4 vertices. The measure of ∠R, ∠S, and ∠T is 112°, 112°, and 68°, respectively.
A quadrilateral is a polygon with 4 number of sides and 4 vertices. A few examples of a quadrilateral are square, rectangle, rhombus, parallelogram, etc.
Since the given quadrilateral is a cyclic quadrilateral, therefore, the sum of the opposite angles of the quadrilateral will be 180°. Therefore, the sum of the ∠R and ∠T can be written as,
∠R + ∠T = 180°
(3x + 40) + (5x − 52) = 180
3x + 40 + 5x - 52 = 180
8x - 12 = 180
8x = 168
x = 24
Now, the measure of angle ∠R and ∠T can be written as,
∠T = 5x − 52 = 5(24) − 52 = 68°
∠R = 3x + 40 = 3(24) + 40 = 112°
Also, the sum of ∠Q and ∠S is 180°. Therefore,
∠Q + ∠S = 180°
68° + ∠S = 180°
∠S = 112°
Hence, the measure of ∠R, ∠S, and ∠T is 112°, 112°, and 68°, respectively.
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