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3 years ago

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

Mathematics

2 answers:

lawyer [7]3 years ago

8 0

Answer:

$x=5$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The <u><em>incenter</em></u> is the point where the three angle bisectors of a triangle meet

therefore

In this problem

$(5x-9)\°=16\°$

Solve for x

$5x=16+9$

$5x=25$

$x=5$

Zinaida [17]3 years ago

4 0

The value of x is 5

<h3>Further explanation</h3>

Firstly , let us learn about trigonometry in mathematics.

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

<h3>sin ∠A = opposite / hypotenuse</h3><h3>cos ∠A = adjacent / hypotenuse</h3><h3>tan ∠A = opposite / adjacent </h3>

Let us now tackle the problem!

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

<em>From the attachment , it can be concluded that:</em>

∠ZAS = ∠ZBS = 90°

∠ZSA = ∠ZSB

ZS of ΔZSA is coincided with ZS of ΔZSB

<em>∴ </em><em>ΔZSA is congruent to ΔZSB</em>

$\texttt{ }$

<em>From the information above , then :</em>

∠ZSA = ∠ZSB

( 5x - 9 )° = ( 16 )°

5x = 16 + 9

5x = 25

x = 25 ÷ 5

$\texttt{ }$

<h2>Conclusion:</h2>

The value of x is 5

$\texttt{ }$

<h3>Learn more</h3>

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

<h3>Answer details</h3>

Grade: College

Subject: Mathematics

Chapter: Trigonometry

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

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