Question

The lesson is 19.2 Angles in inscribed Quadrilaterals

Answer 1

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