Question

find the missing value ​

Answer 1

Answer:

Angle QRS = 180-60 (sum of all angles of triangle is 180 degree)

Angle QRS= 120 degree.

Sum of all angles of triangle is 180 degree

so, angle S + Angle R + Angle x= 180 degree

20 + 120 + angle x= 180

140 + angle x= 180

x =  180- 140 = 40 degrees

Angle QSR is 20 degrees

Angle QSR= Angle y ( because QSR and angle y are opposite angles and opposite angles are equal)

Therefore y = 20 degrees

Now let's find the value of z.

Angle z + Angle y + The third angle ( of triangle PQS) = 180 (the angle sum property.)

In this case, the third angle = x (because x and the third angle in triangle PQS are opposite angles and opposite angles are equal.)

so the third angle = 40 degrees.

the third angle+ angle y +  angle z= 180 degrees (the angle sum property)

40 + 20 + angle z = 180

60 + angle z = 180

angle z = 180 -60 = 120 degree

So, Angle x = 40 degree, angle y = 20 degree, angle z= 120 degree

That's your answer!

Step-by-step explanation:

Answer 2

Answer:

x = 40 , y = 20 and z = 60

Step-by-step explanation:

angle QRS = 180 - 60 (linear pair)

= 120

In triangle QSR,

20 + 120 + x = 180 (Angle sum property)

140 + x = 180

x = 180 - 140

x = 40

PQ || SR,

y = angle QSR = 20 (Vertically opposite angles)

y = 20

Similarly,

z = 60 ( Vertically opposite angles)

Thank you