Question

1. point q is equidistant from the sides of ∠tsr. find m∠rst. (2x + 5)° (5x - 25)°

Explanation:

Step1: Use angle - bisector property

Since point Q is equidistant from the sides of ∠TSR, the ray SQ is the angle - bisector of ∠TSR. So, ∠TSQ=∠RSQ.
We have the equation \(2x + 5=5x-25\).

Step2: Solve the equation for x

Subtract \(2x\) from both sides: \(5 = 5x-2x - 25\), which simplifies to \(5=3x - 25\).
Add 25 to both sides: \(5 + 25=3x\), so \(30 = 3x\).
Divide both sides by 3: \(x = 10\).

Step3: Find the measure of ∠RST

Since ∠RST=∠TSQ + ∠RSQ and ∠TSQ=∠RSQ, and ∠TSQ=2x + 5.
Substitute \(x = 10\) into the expression for ∠TSQ: ∠TSQ=2(10)+5=20 + 5=25°.
Then ∠RST=2∠TSQ=2×25° = 50°.

Answer:

50°