Question

Point Z is the incenter of triangle RST. What is the value of x? x = 2 x = 3 x = 5 x = 8

Answer 1

Answer:

$x=5$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The incenter is the point where the three angle bisectors of a triangle meet

therefore

In this problem

$(5x-9)\°=16\°$

Solve for x

$5x=16+9$

$5x=25$

$x=5$

Answer 2

The value of x is 5

Further explanation

Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

sin ∠A = opposite / hypotenuse

cos ∠A = adjacent / hypotenuse

tan ∠A = opposite / adjacent

Let us now tackle the problem!

The incenter of triangle RST is the intersection between all of the angle bisectors from the three vertices of triangle.

From the attachment , it can be concluded that:

∠ZAS = ∠ZBS = 90°

∠ZSA = ∠ZSB

ZS of ΔZSA is coincided with ZS of ΔZSB

∴ ΔZSA is congruent to ΔZSB

$\texttt{ }$

From the information above , then :

∠ZSA = ∠ZSB

( 5x - 9 )° = ( 16 )°

5x = 16 + 9

5x = 25

x = 25 ÷ 5

x = 5

$\texttt{ }$

Conclusion:

The value of x is 5

$\texttt{ }$

Learn more

• Calculate Angle in Triangle : brainly.com/question/12438587
• Periodic Functions and Trigonometry : brainly.com/question/9718382
• Trigonometry Formula : brainly.com/question/12668178

Answer details

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle , Congruent