Question

point Z is the incenter of triangle SRT , what is the measure of ZTB​

Answer 1

Answer:

31°

Step-by-step explanation:

Sum of interior angles of a triangle = 180

Triangle SRT:

<T = 180 - <S - <R

As you know <S = 24 + 24 = 48°

and <R = 35 + 35 = 70°

So <T = 180 - 48 - 70 = 62°

<ZTB = 1/2 <T

<ZTB = 1/2(62) = 31°

Answer: 31°

Answer 2

Answer:  $\angle{ZTB}=31^{\circ}$

Step-by-step explanation:

• The incenter of the triangle is formed by taking the intersection of the angle bisectors of the three vertices of the triangle.

By angle sum property of triangle , in ΔSRT

$\angle{T}+\angle{S}+\angle{R}=180^{\circ}\\\\\Rightarrow\ \angle{T}+24^{\circ}+24^{\circ}+35^{\circ}+35^{\circ}=180\\\\\Rightarrow\ \angle{T}+118^{\circ}=180^{\circ}\\\\\Rightarrow\ \angle{T}=180^{\circ}-118^{\circ}=62^{\circ}$

Since Z is incenter of ΔSRT, then

$\angle{ZTB}=\dfrac{62^{\circ}}{2}=31^{\circ}$