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 anglework out the size, in degrees, of each angle in the triangle.You must show your working (let X be the smallest angle).
Accepted Solution
A:
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 angleThe third angle is 10° more than the smallest angleThe size of the third angle is xWe 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- Add like terms∴ 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°Learn more:You can learn more about the triangles in brainly.com/question/1479138#LearnwithBrainly