# mat116

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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!!!

• mat116 -

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)

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