A triangle has an angle that measures 80°. The other two angles are in a ratio of 3:7. What are the measures of those two angles?

Question

I need some help to pass my math class because i'm really failing and i need a good education.

Answer 1

Hi there, Nathan!

Let's see if I can help.....

 

All three angles in a triangle must add up to 180 degrees.

We already know one of them.... 80 degrees.

 

If we get rid of that one, we're left with 100 degrees (180 - 80) which represents the other two angles.

 

We know the other two angles are in a ratio of 3:7 which just means 3x and 7x.

We attach the x to help us find the exact degrees of each angle.

And we know these two angle must add up to 100 degrees b/c we subtracted out the third angle we already knew.

 

So, in short....3x + 7x = 100   Now, let's go solve.

 

3x + 7x = 100

10x = 100    we combined like terms

10x/10 = 100/10   we divide each side by 10

x = 10    now we will substitute this value into our two angles to find out exactly how many degrees they each are.

 

3x..... 3(10) is 30 degrees

7x......7(10) is 70 degrees.

 

To check...add up all 3 angles and be sure they equal 180 degrees

30 + 70 + 80 = 180

180 = 180 Check!!

 

 

 

Answer 2

the sum of all angles of the triangle needs to be 180 degrees, meaning that the other two angles combined contain 180 - 80 = 100 degrees between them.

the given 3:7 ratio can be scaled up by 10 to be a 30:70 ratio ... 30 + 70 = 100, meaning that those would be the values of the other two angles ... 30 degrees and 70 degrees