Question

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

Answer 1

Answer:

m∠R = 112°, m∠S = 112°, m∠T = 68°

Step-by-step explanation:

In a cyclic quadrilateral QRST,

m∠R + m∠T = 180° [Since opposite angles of a cyclic quadrilateral measure 180°]

(3x + 40)° + (5x - 52)° = 180°

8x - 12 = 180

8x = 180 + 12

8x = 192

x = 24

m∠R = (3x + 40) = 3×24 + 40

                          = 72 + 40

                          = 112°

m∠T = 180° - m∠R

        = 180° - 112°

        = 68°

Since m∠Q = 68°

m∠S = 180° - m∠Q

        = 180° - 68°

        = 112°

Therefore, m∠R = 112°, m∠S = 112°, m∠T = 68°