Question

Point Z is the incenter of triangle RST.

Point Z is the incenter of triangle S R T. Lines are drawn from the points of the triangle to point Z. Lines are drawn from point Z to the sides of the triangle to form right angles and line segments Z A, Z B, and Z C. Angle A S Z is (5 x minus 9) degrees and angle Z S B is 16 degrees.
What is the value of x?

x = 2
x = 3
x = 5
x = 8

Answer 1

The incenter Z lies on the angle bisector of angle RST, so SZ bisects angle S. Therefore angle ASZ = angle ZSB. Set 5x − 9 = 16.

5x − 9 = 16
5x = 25
x = 5

Answer: x = 5.