Triangle $PQR$ is isosceles and the measure of angle $R$ is $40^\circ$. The possible measures of angle $P$ are $x, y,z$. What is the value of the sum $x y z$

The possible value for angle P will be 100

And sum will  also 100 because it has only one value.

Step-by-step explanation:

Given:

angle R measures 40 degree  and PQR is isosceles triangle.

To Find:

Measure angle P.

Solution:

The given triangle is isosceles hence it will have 2 same angle included in it.

And sum of all angles of a triangle is 180 degree.

let same angles be x and other be y

So ,

x+x+y=180 sum of all angles.

2x+y=180.

Now to find possible values for y ,with x=40,

2x+y=180

80+y=180

y=100

So being x= 40 y =100  which satisfy given angle R condition.

now let y=80,then x should satisfy 40 degree value, so

2x+80=180

2x=100

x=50

it doest not satisfy the given value hence possible for  y will be 100.

Since x=40 degree.