Question

Note: Figure not to scale What is the measure of the angle marked y?

Answer 1

Answer:

y = 48°

Step-by-step explanation:

In parallelogram STVU,

$m\angle TVU + 60\degree = 180\degree$ (linear pair angles)

$m\angle TVU = 180\degree - 60\degree$

$m\angle TVU = 120\degree$

$m\angle UST= m\angle TVU =120\degree$(Opposite angles of a parallelogram)

$m\angle USR= 120\degree(\because S-R-T)$

$108\degree + m\angle USR+m\angle PSR= 360\degree$

$108\degree + 120\degree+m\angle PSR= 360\degree$

$228\degree + m\angle PSR= 360\degree$

$m\angle PSR= 360\degree - 228\degree$

$m\angle PSR= 132\degree$

$y+m\angle PSR= 180\degree$

(Adjacent angles of a parallelogram)

$y+ 132\degree= 180\degree$

$y= 180\degree-132\degree$

$y= 48\degree$