Question

the vertex angle of an isosceles triangle measure eight times the measure of a base angle. Find the measure of a base angle.
A.18
B.24
C.36
D.43

Answer 1

Didn't we work on this very same problem a minute or two back? Or was that another O. S. user?

Answer 2

i acidentlly closed it

Answer 3

Try your utmost to remember what was said in that post. You'll need to set up an equation in the variable x.

Start by representing each of the 2 base angles by x. What is an appropriate representation of the vertex angle if the vertex angle is 8 times the measure of one of the base angles?

Write your equation. these 3 angles add up to what?

Answer 4

so the equation would be 1/2 times base times height

Answer 5

No: that's the formula for the area of a triangle.

Maybe you should draw the triangle in question. Note that it's isosceles. What does that mean?

Answer 6

an isosceles triangle has two equal sides right

Answer 7

Right, and so the base angles are equal.

Represent each of the base angles with a letter. What'll it be?

Answer 8

x

Answer 9

Great. What represents the measure of the other base angle?

Answer 10

vertex

Answer 11

Yes, but that vertex angle is measured (e. g., in degrees or in radians). We have to represent it algebraically. How large does the problem statement say this angle is?

Answer 12

8 times the measure

Answer 13

Right. 8 times the measure of ... what?

Answer 14

the base angle

Answer 15

One of the base angles. if one base angle is represented by x, what is 8 times that?

Answer 16

8

Answer 17

8 times what?

The measure of one of the base angles is x.
The measure of the vertex angle is 8 times that. Represent the measure of the vertex angle here, please.

Answer 18

8x

Answer 19

Very good. Now, you have three angles inside this triangle. They are x, x and 8x. Add those together and set your sum equal to ... what value?

Answer 20

2x+8x=180?

Answer 21

Yes, and 2x + 8x = ?

Answer 22

10x?

Answer 23

Yes, and so 10x = ?

Answer 24

18?

Answer 25

Yes, and now we have to check that. We know that x plus x plus 8x should equal 180 deg. Subst. 18 for x in that statement. Does it hold true, or not?

Answer 26

18+18+8*18=180

Answer 27

36+8*18 = ?

Answer 28

180

Answer 29

And so x=18 degrees is correct!

Answer 30

yes thank u for ur time my teacher doents teach she shows us videos

Answer 31

Happy to be of help, Hannah! Bye for now!

Answer 32

bye