Question

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

Answer 1

Answer:

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

Step-by-step 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:

$\angle\,B=\frac{216^o}{2} =108^o$