Question

1. if z is the midpoint of rt, what is the measure of rt?

a. 119
b. 17
c. 192
d. 73

1. ray sq bisects ∠rst and the measure of ∠rsq = 4x - 8. which expression represents ∠rst?

a. 4x - 8
b. 2x - 4
c. 8x - 16
d. x - 4

Explanation:

Question 3

Step1: Use the mid - point property

Since \(Z\) is the mid - point of \(RT\), then \(RZ = ZT\). So, \(7x−23 = 96\).

Step2: Solve for \(x\)

Add \(23\) to both sides of the equation \(7x−23 = 96\):
\(7x=96 + 23\)
\(7x=119\)
Divide both sides by \(7\): \(x = 17\).

Step3: Calculate \(RT\)

\(RT=RZ + ZT\). Since \(RZ = ZT = 96\) (from the mid - point property), \(RT=96+96\)

Step1: Use the angle - bisector property

If a ray \(SQ\) bisects \(\angle RST\), then \(\angle RST=2\angle RSQ\)

Step2: Substitute the given expression for \(\angle RSQ\)

Given \(\angle RSQ = 4x−8\), then \(\angle RST=2(4x - 8)\)

Step3: Simplify the expression

Using the distributive property \(a(b - c)=ab−ac\), where \(a = 2\), \(b = 4x\), \(c = 8\)
\(\angle RST=2\times4x-2\times8=8x - 16\)

Answer:

\(192\) (Option C)

Question 4