Question

is p is parallel to q is parallel to r ..find x y and z in the following figure​

Answer 1

Answer:

Step-by-step explanation:X = 55° ..Alternate angels

y + 55 =180 interior angles

y=180-55

y=125

z+90+55=180 sum of measures of all angles of triangle is 180

z+145=180

z=180-145

z=35

Answer 2

x = 55 degree

y = 125 degree

z = 35 degree

Step-by-step explanation:

The most important point here is that: If p||q and q||r , then p||r

For z

Since p||r therefore,

90degree + 55 + z = 180degree (co-interior angles)

145 + z = 180

=> z = 180 - 145

=> z = 35 degree

For y

Since p||q , therefore,

55degree + y = 180degree (co-interior angles)

=> y = 180 - 55

=> y = 125 degree

For x

Since the fig. with angles z , x and 90degree is a triangle ,therefore,

90degree + z + x = 180degree (Angle sum property of a triangle)

=> 90 + 35 + x = 180

=> 125 + x = 180

=> x = 180 - 125

=> x = 55degree

(Note: We can directly find the value of x as 55degree as the 55degree angle is alternate to x)