In a triangle, the measure of the 2nd angle is twice the 1st angle. The 3rd angle is 15 degrees less than the 2nd angle. If there are 180 degrees in a triangle, find the measure of each angle.

Question

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Answer 1

X = first angle, 2x= second angle, 2x-15 . Their sum is 180. Solve for x. I got x= 39.  Plug 39 to x to get 2 (39) to get second angle =78. To get third angle subtract 15 to get 63. First angle=39. Second angle =78. Third angle = 63.

Answer 2

In a triangle, the measure of the 2nd angle is twice the 1st angle. The 3rd angle is 15 degrees less than the 2nd angle. If there are 180 degrees in a triangle, find the measure of each angle.

The triangle is ABC, with associated angles α,  β,  γ.

Using the given information

the 2nd angle is twice the 1st angle -> β = 2α

The 3rd angle is 15 degrees less than the 2nd angle -> γ = β - 15

there are 180 degrees in a triangle -> α +  β + γ = 180

Our three simultaneous eqns then are,

 β = 2α    --------------------- (1)

γ = β - 15    ------------------ (2)

α +  β + γ = 180   ---------- (3)

Substituting for (1) into (2) and (3),

γ = 2α - 15    ------------------ (4)

α +  2α + γ = 180   ---------- (5)

rearranging,

γ - 2α = -15    ----------------- (6)

γ + 3α = 180   ---------------- (7)

Subtracting (6) from (7),

5α = 195

α = 39

β = 78

γ = 63

The solution then is: α = 39, β = 78, γ = 63

Answer 3

Let first angle = x

Second angle = 2x

Third angle =2x-15

x+2x+2x-15=180
x=39
2x=78
2x-15=63

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Answer 4

Solution: Let one angle be x, another be 2x and the other one be 2x-15 Now, we have, x+2x+2x-15=180 ( sum of interior angles or, 5x-15= 180 of a triangle is 180) or, 5x=180+15 or, 5x=195 or, x=195/5 so, x=39 Hence, one angle=39 another =2×39=78 other one=2×39-15 =78 -15 =63