Question

T
P
In the given figure, find ZPQR.
20 - XºR
X + 70°
S-
R
Q​

Answer 1

As EF is a transversal, we can say the following:

∠APQ=∠CQF (corresponding angles are equal)    (1)

∠CQP+∠CQF=180  

o

 (linear pair of angles)    (2)

x+y+z=180  

o

 (sum of angles of a triangle is 180  

o

)   (3)

Using (1):

30  

o

+y=65  

o

⟹y=35  

o

 

Using (2):

65  

o

+25  

o

+z=180  

o

⟹z=90  

o

 

Using (3):

35  

o

+90  

o

+x=180  

o

⟹x=55  

o

 

Final answer:

x=55  

o

,y=35  

o

,z=90  

o