measure each base angles an isosceles triangle 9 degrees < 4 times measure vertex angle. ea. base angle=, vertex angle=

Question

to find measures of the angles of each triangle

Answer 1

We know a couple of things here.

 

1) the sum of the measure of the angles of a triangle is 180^o.

2) Since this is an isosceles triangle, we can define the vertex angle as V and the two base angles as B.  This translates mathematically to V + 2B = 180^o.

3) Also, B + 9 = 4V, or B = 4V - 9

 

We can use the info in 3) and substitute it into the equation in 2) like this.

V + 2B = 180  For now I'm leaving off the degree symbol.

Since B = 4V - 9, we can use this value of B in the equation above

V + 2(4V -  9) = 180

 

We now have an equation with only one variable, the Vertex angle, V.  And can solve for V.

V + 8V - 18 = 180

9V = 198

V = 22  So the vertex angle = 22^o

 

Since B = 4V - 9

B = 4 (22) - 9 = 88-9=79

So each base angle is 79^o

 

Let's check to see if this is correct.

Does 79 + 79 + 22 = 180?

 

It does.

 

Hope this has helped you.

 

Answer 2

We are talking about an isosceles triangle so two base angles are same

base angle = 4*vertical -9

Since we don't know the degree of the vertical angle, let's set that to a variable x.

if you rewrite the base angle with x 

base angle = 4x-9

we know that the total degree of a trangle is 180

so we can set up an equation as 3 angles added together = 180

2*base angle + vertical angle= 180

2*(4x-9) + (x)= 180

let's combine the like terms

8x -18 +x = 180

9x = 198

now we continue with the algebra and solve for x by itself

x = 22 degrees 

x = vertical = 22 (answer for vertical angles)

whereas the base angles 4x-9 when you plug in 19.8 in for  = 79 degrees (answer for base angles)

Check = 2*(4(22)-9) + (22) = 180 

180 = 180