Question

In quadrilateral QRST, Angle R S T measures (5x 15)°. Angle TQR measures (4x 3)°. Circle P is inscribed with quadrilateral Q R S T. What is the measure of angle RST? 15° 75° 105° 165°.

Answer 1

Answer:

  (c)  105°

Step-by-step explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

  (5x +15) +(4x +3) = 180

  9x +18 = 180 . . . . . simplify

  x +2 = 20 . . . . . . . divide by 9

  x = 18 . . . . . . . . . . subtract 2

Angle RST is ...

  5x +15 = 5(18) +15 = 105

The measure of angle RST is 105°.