Question

What is the measure of ZA? What is the measure of ZB?

Answer 1

Answer:

$m\angle A = 72\degree \\m\angle B = 108\degree$

Step-by-step explanation:

ABCD is a parallelogram.

Since, opposite angles of a parallelogram are congruent.

$\therefore m\angle A = m\angle C\\\therefore (5y-3)\degree = (3y+27)\degree \\\therefore 5y - 3= 3y +27\\\therefore 5y-3y = 27+3\\\therefore 2y = 30\\\\\therefore y = \frac{30}{2} \\\\\therefore y = 15\\\because m\angle A = (5y-3)\degree \\\therefore m\angle A = (5\times 15-3)\degree \\\therefore m\angle A = (75-3)\degree \\\huge{\red {\boxed {\therefore m\angle A = 72\degree}}} \\\\\because m\angle A + m\angle B = 180\degree(opposite \: \angle 's\: of\:a\: \parallel ^{gm}) \\\therefore m\angle B = 180\degree - 72\degree \\\huge{\purple {\boxed {\therefore m\angle B = 108\degree}}}$