Question

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

Answer 1

31°

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)`

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}=(62^(\circ))/(2)=31^(\circ)`