Question

The size of the largest angle in a triangle is 3 times the size

of the smallest angle.
The third angle is 10° more than the smallest angle.
Work out the size, in degrees, of each angle in the triangle.
You must show your working (let x be the smallest angle).
Show your working

Answer 1

• smallest angle = 34 degrees
• largest angle = 102 degrees
• third angle = 44 degrees

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Work Shown:

• x = smallest angle
• 3x = largest angle
• x+10 = third angle

For any triangle the three inside angles add to 180.

(x)+(3x)+(x+10) = 180

5x+10 = 180

5x = 180-10

5x = 170

x = 170/5

x = 34

We can use this to find the missing angles.

• x = 34 = smallest angle
• 3x = 3*34 = 102 = largest angle
• x+10 = 34+10 = 44 = third angle

Check: 34+102+44 = 180 which confirms the answers are correct.