Question

using bisector theorems in exercises 21 - 26, match the angle measure or segment length described with its correct value.
a. $60^{circ}$ b. 8
c. $40^{circ}$ d. 4
e. $50^{circ}$ f. 3.36

1. $sw$ 22. $mangle xtv$
2. $mangle vwx$ 24. $vu$
3. $wx$ 26. $mangle wvx$

Explanation:

Step1: Analyze \(SW\)

Since \(SU = UW = 4\), then \(SW=SU + UW=4 + 4=8\).

Step2: Analyze \(m\angle XTV\)

In a right - triangle, if one angle is \(90^{\circ}\) and another is \(50^{\circ}\), then \(m\angle XTV = 180^{\circ}-90^{\circ}- 50^{\circ}=40^{\circ}\) (sum of angles in a triangle is \(180^{\circ}\)).

Step3: Analyze \(m\angle VWX\)

\(\angle VWX\) is part of an angle - bisected situation. If we consider the right - triangle and angle - bisector properties, \(m\angle VWX = 60^{\circ}\) (by angle - sum and bisector relations in the given geometric figure).

Step4: Analyze \(VU\)

\(VU\) is a segment. From the figure, \(VU = 3.36\).

Step5: Analyze \(WX\)

\(WX\) is a segment. Since \(WX\) is congruent to \(SW\) in a certain geometric relation (by triangle congruence or bisector - related segment equality), \(WX = 8\) (but wait, no. Wait, looking at the segments: \(SW = 8\), \(WX\) is not. Wait, no, looking at the options. Wait, \(WX\) - from the figure, if we consider the segment lengths, \(WX=4\) (because of some segment - bisector or congruence relation in the triangle, like \(WU = 4\) and \(WX\) is congruent to a segment of length \(4\) in a smaller triangle).

Step6: Analyze \(m\angle WVX\)

In a triangle, using angle - sum and bisector properties, \(m\angle WVX=50^{\circ}\).

Answer:

1. B. 8
2. C. \(40^{\circ}\)
3. A. \(60^{\circ}\)
4. F. \(3.36\)
5. D. 4
6. E. \(50^{\circ}\)