Question

In quadrilateral QRST, m∠Q > is 68°, m∠R is (3x + 40)°, and m∠T is (5x − 52)°. What are the measures of ∠R, ∠S, and ∠T? Write the numerical values in that order with the measures separated by commas.

Answer 1

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.

What is a quadrilateral?

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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