In a triangle ABC, angle B is 4 times angle A and angle C is 16 degrees less than 5 times angle A.
What is the size of angle A _____
B _____ and C _____
I would like to learn this so please be so kind to walk me through the steps. I appreciate you very much!!!
Sure! I'd be happy to help you solve this problem step by step.
Let's assign a variable to angle A. Let's say angle A = x.
Now, we're given that angle B is 4 times angle A, so angle B = 4x.
We're also given that angle C is 16 degrees less than 5 times angle A, so angle C = 5x - 16.
In any triangle, the sum of all three interior angles is always 180 degrees. So we can write an equation using this fact:
angle A + angle B + angle C = 180
Now we substitute the values we found:
x + 4x + (5x - 16) = 180
Now let's simplify the equation:
x + 4x + 5x - 16 = 180
10x - 16 = 180
To solve for x, we'll isolate the variable:
10x = 180 + 16
10x = 196
Now divide both sides of the equation by 10 to solve for x:
x = 196 / 10
x = 19.6
Now we can find the values of all three angles:
Angle A = x = 19.6 degrees
Angle B = 4x = 4 * 19.6 = 78.4 degrees
Angle C = 5x - 16 = 5 * 19.6 - 16 = 68 degrees
Therefore, the size of angle A is 19.6 degrees, angle B is 78.4 degrees, and angle C is 68 degrees.
make a diagram, it does not have to be to scale.
let angle A = x
(I picked A since both conditions stated used it as a reference)
"angle B is 4 times angle A" ---> angle B = 4x
"angle C is 16 degrees less than 5 times angle A" -->angle C = 5x - 16
Now, what do you know about the 3 angles of a triangle?
Don't they add up to 180° ?
so x + 4x + 5x-16 = 180
10x = 196
x = 19.6°
So by the definitions above
A = 19.6
B = 78.4
C = 82
(check for their sum)