## 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 an

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).​

in progress 0
2 days 2021-10-13T02:09:10+00:00 1 Answer 0

1. The sizes of the angles are 34° , 44° , 102°

Step-by-step explanation:

The given is:

• 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
• The size of the third angle is x

We need to find the size of each angle in the triangle

∵ The size of the smallest angle = x°

∵ The size of the largest angle is 3 times the size of the smallest angle

∴ The size of the largest angle = x × 3 = (3x)°

∵ The third angle is 10° more than the smallest angle

∴ The size of the third angle = (x + 10)°

Add the size of the three angles and equate the sum by 180°

∵ The sum of the sizes of the interior angles of a Δ is 180°

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

∴ x + 3x + x + 10 = 180

∴ 5x + 10 = 180

– Subtract 10 from both sides

∴ 5x = 170

– Divide both sides by 5

x = 34

∵ x is the size of the smallest angle

∴ The size of the smallest angle is 34°

∵ 3x is the size of the largest angle

∴ The size of the largest angle = 3(34) = 102°

∵ x + 10 is the size of the third angle

∴ The size of the third angle = 34 + 10 = 44°

The sizes of the angles are 34° , 44° , 102°