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help me with angles of a triangle

+7 votes
104 views
asked Oct 12, 2017 in Math by Friends come and go (3,300 points)
this is ixls that I have to do and we had a sub today and he couldn't help me wid it so here it is "One angle of a triangle measures 100°. The other two angles are in a ratio of 3:13. What are the measures of those two angles?"


1 Answer

+2 votes
answered Oct 12, 2017 by whizkid (65,600 points)
selected Oct 12, 2017 by Friends come and go
 
Best answer

You have a triangle with one angle at 100º and the other two angles have a ratio of 3:13.

You can first set variables for the 3 angles. a, b, c

a = 100  (angle you know)

b = ?

c = ?

We have 2 unknowns (b and c), so we must have at least 2 equations to solve it.

We know that the sum of all angles in any triangle is 180 degrees, so that is one equation.

Equation 1: a + b + c = 180

You also gave the ratio of 3:13 for angles b and c (the unknowns) for the other equation

Equation 2: 3/13 = b/c

Multiply both sides of the above by 'c' to get

c(3/13) = (b/c)c

The c on the right cancels and we are  left with

b = 3c/13

Next, substitute b  and a in the first equation

a + b + c = 180

a = 100

b = 3c/13

100 + 3c/13 + c = 180

subtract 100 from  both sides

3c/13 + c = 80

multiple both sides by 13 to clear the fractions

13(3c/13) + 13c = 80(13)

3c + 13c = 1040

add left side

16c = 1040

c = 1040/16

c = 65º

You can now find b using the first or second equation. The first is easier, but best to use both to check your  work.

a + b + c = 180

b = 180 - c - a

b = 180 - 65 - 100

b = 15

Second Equation Check

 3/13 =b/c

let c = 65

3/13 = b/65

b = 3(65)/13 = 15 (second check)

Answer: a = 100, b = 15, c = 65

 

commented Oct 26, 2019 by KITTEN (616,760 points)
You're a whiz, whizkid!

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