Question

The size of the largest angle in a triangle is 4 times the size of the smallest angle. The other angle is 27 degrees less than the largest angle.

Work out, in degrees, the size of each angle in the triangle.

Answer 1

Answer: 23°, 65° and 92°

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