Question

find the values of x, y, z in the following figure

Answer 1

angles opposite to equal sides are equal in a triangle

exterior angle =sum of two opposite interior angles in a triangle

inPQS,PS=QS

so,x=40°

z is exterior angle toPQS

z=40°+40°=80°

in PSR,PR=SR

y=80°

Answer 2

Answer:

x = 40, y = 50, z = 80

Step-by-step explanation:

x = 40 degrees because the triangle it is in is an isosceles triangle (two sides are the same) that means the two angles on the two identical sides is the same.

y is because we know x and we know one of the angle of the big triangle so when you take that away from 180 (the total degrees of a triangle is 180) it leaves 100 and because we have another isosceles so y is the same the angle of the big triangle that is still unknown so we divide 100 by 2 this equals 50 so y is 50.

z is 80 because if we have a look at the right small triangle it has 2 known angles, y and the other one. because a triangle has a total degrees of 180 we take the two known angles away from 180 which leaves 80. (180 - 50 - 50)