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The angle measures of the three angles of a triangle are in the ratio $1:3:6$. What is the number of degrees in the measure of the largest angle?

The number of degree in the measure of the largest angle is 108

Step-by-step explanation:

The sum of the measures of the interior angles of a triangle is 180°

∵ The angle measures of the three angles of a triangle are in

   the ratio 1 : 3 : 6

∴ The sum of the ratio = 1 + 3 + 6 = 10

∵ The sum of the measures of the interior angles of a triangle = 180°

- Let us use the ratio method

→  ∠1  :  ∠2  :  ∠3  :  sum

→  1     :  3    :  6     :  10

→  x     :  y    :  z     :  180°

By using cross multiplication

∵ 10 × x = 1 × 180

∴ 10 x = 180

- Divide both sides by 10

∴ x = 18

∴ m∠1 = 18°

∵ 10 × y = 3 × 180

∴ 10 y = 540

- Divide both sides by 10

∴ y = 54

∴ m∠2 = 54°

∵ 10 × z = 6 × 180

∴ 10 z = 1080

- Divide both sides by 10

∴ z = 108

∴ m∠3 = 108°

The number of degree in the measure of the largest angle is 108