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The measure of angle a is twice the measure of angle b the measure of angle c is at least one degree more than the measure of angle a if the sum of the three angles is at least 61 degrees what is the range possible measurements for angle b

Respuesta :

Answer:

Step-by-step explanation:

The measure of angle a is twice the measure of angle b. This means that

a = 2b

The measure of angle c is at least one degree more than the measure of angle a. This means that

c ≥ a + 1

c ≥ 2b + 1

if the sum of the three angles is at least 61 degrees, it means that

a + b + c = 61 - - - - - - - - - - - - - 1

Substituting a = 2b and c = 2b + 1 into equation 1, it becomes

2b + b + 2b + 1 = 61

5b = 61 - 1 = 60

b = 60/5 = 12

c ≥ 2× 12 + 1

c ≥ 25

25 ≥ a + 1

25 - 1 ≥ a

24 ≥ a

a ≤ 24

Therefore, the range possible measurements for angle b is

b ≤ 12

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