Geometry Help?

A:B = 4:5
A = 4x
B = 5x

180-81.9 = 98.1
4x+5x = 98.1
x = 10.9

A = 4x = 43.6°
B = 5x = 54.5°

Let 4y° and 5y° be the two unknown angles in the triangle.

Sum of interior angles of a triangle :
4y + 5y + 81.9 = 180
9y = 98.1
y = 10.9
4y = 43.6
5y = 54.5

The other two angles are 43.6° and 54.5°.

These are exactly the same as other questions that you've asked. Are you learning from them or are we just doing your homework for you?

Since the sum of all angles in a triangle is 180 and you know one angle is 81.9, then the sum of the other two are:

180 - 81.9 = 98.1

So we have two angles that add to that:

x + y = 98.1

And the two angles are in a ratio of 4:5, so:

x/y = 4/5

We now have a system of equations that we can solve. Let's simplify the second equation by multiplying both sides by y, and solve for x in the first equation by subtracting y from both sides:

x = 98.1 - y and x = 4y/5

Both of the right sides are equal to x, so both of the right sides are equal to each other:

98.1 - y = 4y/5

Multiply both sides by 5:

490.5 - 5y = 4y

Add 5y to both sides:

490.5 = 9y

Divide both sides by 9:

y = 54.5

Now that we have y, solve for x:

x = 98.1 - y
x = 98.1 - 54.5
x = 43.6

Your other two angles are:

43.6 and 54.5 degrees

Given angle is 81.9°
Other angles add up to 98.1
9______________98.1
1______________10.9
4______________43.6
5______________54.5

Angles are 43.6° , 54.5° and 81.9°

180 - 81.9 = 98.1

The angles are 4/9 * 98.1 and 5/9 * 98.1

4/9 * 98.1 = 43.6°

5/9 * 98.1 = 54.5°