Question

What is the measure of angle A ?
what is the measure of angle B ?

Answer 1

`\angle\,A=72^o\\\angle\,B=108^o`

Explanation:

Notice that buy construction of a parallelogram,the angles
`\angle \,A` and
`\angle \,C` must equal each other. Then, based on the info given, we can write the following equation:

`3\,y+27^o=5\,y-3^o\\27^o+3^o=5\,y-3\,y\\30^o=2\,y\\y=15^o`

Then, angle
`\angle \,A` =
`5\,(15^o)-3^o=72^o` which is also equal to angle B

and since the addition of all internal angles of the parallelogram must equal
`360^o` , then:

`B+D=360^o-72^o-72^o=216^o`

and therefore, since
`\angle \,B` and
`\angle \,D` must be equal, then:

`\angle\,B=(216^o)/(2) =108^o`