Answer:
[tex]A=91^o[/tex]
[tex]B=146^o[/tex]
[tex]C=89^o[/tex]
[tex]D=34^o[/tex]
Step-by-step explanation:
we know that
In an inscribed quadrilateral ABCD opposite angles are supplementary
so
[tex]A+C=180^o[/tex] ----> equation 1
[tex]B+D=180^o[/tex] ----> equation 2
step 1
Find the value of x
substitute the given values in equation 1
[tex](2x+3)^o+(2x+1)^o=180^o[/tex]
[tex]4x=180-4\\4x=176\\x=44[/tex]
step 2
Find the measure of angle A,C and D
substitute the value of x
[tex]A=(2(44)+3)=91^o[/tex]
[tex]C=(2(44)+1)=89^o[/tex]
[tex]D=(44-10)=34^o[/tex]
step 3
Find the measure of angle B
Remember the equation 2
[tex]B+D=180^o[/tex] ----> equation 2
substitute the value of D
[tex]B+34^o=180^o[/tex]
[tex]B=180^o-34^o=146^o[/tex]
