Answer:
m<R=44.9,m<S=56.9,m<T=44.9,m<U= 32.9.
Step-by-step explanation:
When two chords are equal then the measure of the arcs are equal.
Chord RU= Chord UT
Or , m arc RU= m arc UT,
3z-4=x+2z+7 Or z=x+11
Chord RS=Chord ST ,
m arc RS=m arc ST=3x+5
Sum of m arc in a circle =360 degrees.
Or ,
3x+5+3x+5+3z-4+x+2z+7=360
7x+5z+13=360
Substituting z=x+11
7x+5(x+11)+13=360
7x+5x+55+13=360
12x+68=360
12x=292,x=24.3
z=x+11=11+24.3=34.3
m arc RU=marc UT= 3z-4=3(24.3)-4=69
m arc RS =marc ST= 3x+5=3(24..3)+5=77.9
m<R= (marc UT+ m arc ST)÷2
m<R=(69+77.9)÷2=73.45
m<S= (m arc RU+m arc UT)÷2
m<S= (69+69)÷2=69
m<T=(m arc RU+m arc RS)÷2=73.45
m<U=(m arc RS+m arc m arc ST)÷2=77.9
The angles opposite equal sides are also equal. The sum of angles in a triangle is 180. So 2x + 27 + 2x + 27 + 3x + 28 = 180.
7x + 82 = 180
7x = 98
x = 14
Now plug x into each angle to find their measures.
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