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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.​

Respuesta :

Answer: 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

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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