Question

The measure of each of the base angles of an isosceles triangle is 9° less than 4 times the measure of the vertex angle. Plz explain how to find also

Answer 1

Isocoleese means that 2 sides are the same legnth
that also means that 2 angles are the same legnth
so represent the angles as x,y,z
the vertex is the different angle
lets says that x=y because they are the 2 same angle and z=vertex
so just do
the angles measure x,x,z because x=y
so
base angle=x=y
remember that all 3 inside angles added together equals 180 so
x+y+z=180 or x+x+z=180
so we have

measure of each of the base angles of the isosolese triangle is 9 les than 4 times the vertex
that means that x is 9 less than 4 times z or x=-9+4z or x=4z-9
so we have the other equation
x+x+z=180
subsitute 4z-9 for x
4z-9+4z-9+z=180
group like terms
4z+4z+z-9-9=180
add like terms
9z-18=180
add 18 to both sides
9z=198
divide both sides by 9
z=22
subsitute
x=4z-9
x=4(22)-9
x=88-9
x=79

x=y=79


the angles are
base angles=79 degrees
vertex=22 degrees


x=79
y=79
z=22