Question

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?

Answer 1

Concept

The incenter of a triangle is the point at which the triangle's three interior angle bisectors intersect. This point is equidistant from the triangle's sides because the junction point of the central axis is the centre point of the triangle's inscribed circle. Because the largest circle can fit inside a triangle, the incenter of a triangle is also known as the centre of a triangle's circle. An incircle of a triangle is a circle that is inscribed within a triangle. The letter I is commonly used to represent the incenter. If ΔPQR be a triangle and I be the incentre, then ∠PQI = ∠IQR, ∠QPI = ∠RPI ∠PRI = ∠QRI.

Given

• Z is incentre of ΔSRT

• To form right angles and line segments ZA, ZB, and ZC, lines are drawn from point Z to the triangle's sides.

• ∠AZR = 35°, ∠ZRC = 35°

• ∠BSZ = 24°, ∠ZSA = 24°

Find

We have to find the value of the angle ∠ZTB.

Solution

Here, ∠SRT = 2 * 35 = 70

∠RST = 2 * 24 = 48

∠RTS = 180 - (70 + 48) = 180 - 118 = 62

Then ∠ZTB = 62/2 = 31

Therefore, the value of the angle ∠ZTB = 31°

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