Point Z is the incenter of ΔSRT.

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 Z R is 35 degrees. Angle Z R C is 35 degrees. Angle B S Z is 24 degrees. Angle Z S A is 24 degrees.
What is mAngleZTB?

24°
31°
35°
62°

Point H is the center of the circle that passes through points D, E, and F.
Point H is the center of the circle that passes through points L, M, and N.
Line segment H E is-congruent-to line segment H D
Line segment L H is-congruent-to line segment N H
Line segment F L is-congruent-to line segment F N

A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.

For the given situation,

Let S R T be a triangle, and point Z is the in center of triangle S R T.

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 as shown in the below figure.

Here, ∠ AZR = 35°, ∠ZRC = 35°, ∠ BSZ = 24°, ∠ZSA = 24°, ∠ZTB = ?

The in center of a triangle is the intersection point of all the three interior angle bisectors of the triangle. It can be defined as the point where the internal angle bisectors of the triangle cross.

According to the angle bisector theorem,

⇒ [tex]\angle ZRC = \angle ARZ[/tex]

⇒ [tex]\angle ARZ = 35\degree[/tex]

Let the unknown angle, ∠ZTB be x. Then ∠BTC = 2x

The sum of the interior angles of a triangle is equal to 180°,

So, [tex]24+24+35+35+2x=180[/tex]

⇒ [tex]118+2x=180[/tex]

⇒ [tex]2x=180-118[/tex]

⇒ [tex]x=\frac{62}{2}[/tex]

⇒ [tex]x=31[/tex]

Hence we can conclude that the measure of angle ∠ZTB of triangle SRT is 31°.

Learn more about triangles here

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