The size of the largest angle in a triangle is 4 times the size of the smallest angle.
The other angle is 27° less than the largest angle.
Work out, in degrees, the size of each angle in the triangle.
You must show your working.

The size of each angle in the triangle in degrees are 23°, 92° and 65°

The sum of angles in a triangle = 180

Therefore

let

the largest angle = x

the smallest angle  = y

Therefore,

x = 4y

Let the last angle = z

Therefore,

z = x - 27

Therefore,

x + y + z = 180

x + y + x - 27 = 180

2x - 27 + y = 180

2x + y = 207

2(4y) + y = 207

8y + y = 207

y = 207 / 9

y = 23°

x = 4y

x = 4(23)

x = 92°

z = x - 27

z = 92 - 27

z = 65°

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23°, 65° and 92°

Step-by-step explanation:

a + b + c = 180 (The angles of a triangle equals to 180)

a = 4c (the largest angle is 4 times the smallest angle)

b = 4c - 27 (the final angle is 27 less than the largest angle)

c = c

Now that we have gotten the values for the variables in our equation, we plug them in:

4c + 4c - 27 + c = 180

Combine like terms:

4c + 4c + c - 27 = 180

9c - 27 = 180

9c = 180 + 27

9c = 207

Divide both side by 9

c = 23

a= 4c

a = 4 × 23

a = 92

b = 4c - 27

b = 92 - 27

b = 65

b = 65

Check:

a + b + c = 180

92 + 65 + 23 = 180

180 = 180

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step-by-step explanation:

1+2+3+4+5+6+7+8+9+10 = 55

2*10 = 20

55-20 = 35