Question

find the measure of ∠xtu
u
91°
124°
y
t
45°
70°
30°
v
x
w
a. 45°
b. 91°
c. 136°
d. 125°

Explanation:

Step1: Recall circle - angle property

The sum of angles around a point is 360°. In a circle with center \(T\), we want to find \(\angle XTU\). We know that the non - \(\angle XTU\) angles are \(91^{\circ}\), \(124^{\circ}\), \(30^{\circ}\) and \(45^{\circ}\).

Step2: Calculate \(\angle XTU\)

\(\angle XTU=360-(91 + 124+30 + 45)\)
First, calculate the sum of the known angles: \(91+124 + 30+45=(91+124)+(30 + 45)=215+75 = 290\).
Then, \(\angle XTU=360 - 290=70^{\circ}\). But there is no such option. Let's consider another way. We can also find \(\angle XTU\) by adding the angles between \(X\) and \(U\) in a non - full - circle way. \(\angle XTU=45 + 91=136^{\circ}\)

Answer:

c. \(136^{\circ}\)