Triangles-Angles...Help me!?

Question

1) In a triangle one angle is 15 degrees more than the measure of the second angle.
The third angle is 30 degrees less than the measure of the second angle. Find the measure of the third angle.

Answer 1

Let the second angle be x derees
therefore the other two angles are x+15 and x-30
therefore,
x+x+15+x-30=180
or,3x=180-15+30=195
or x=65
therefore,the angles are 65 degrees,80 degrees and 35 degrees respectively

Answer 2

you know the interior angles of a triangle = 180 degrees:

a + b + c = 180 where a, b, c are the angles.

you also know:

b + 15 = a (one angle is 15 deg. more than the 2nd)

and

b - 30 = c (3rd angle is 30 deg less than 2nd)

Now, you have 3 eqns and 3 unknowns:

a + b + c = 180
b + 15 = a
b - 30 = c

So, using the 2nd and 3rd eqns, plug those values in to the 1st eqn:

(b+15) + b + (b - 30) = 180

3b - 15 = 180
b = 65

Now plug this back into the 2nd and 3rd eqns to find a and c:

b + 15 = a
65 + 15 = a
a = 80

and

b - 30 = c
65 - 30 = c
c = 35

Therefore,

a = 80
b = 65
c = 35

Check:

80 + 65 + 35 = 180...

Answer 3

Let the measures of the three angles be x, y, and z, respectively.
x=15+y......(1)
z = y-30......(2)
x+y+z = 180......(3)
(1)-(2)
x-z = 45......(4)
Plug in (2) and (4) in (3)
z+45 + z+30 + z = 180
Solve for z,
z = 35, the third angle measure.

Answer 4

let's say the second angle is x degrees

and we all know that the SUM of all the angles of the triangle is 180 degrees

so ...

(x+15) is the first angle
x is the second angle
and (x-30) is the third angle

(x+15) + x + (x-30) = 180

in other words
3x -15 = 180

3x = 195

x = 195/3 = 65 degrees

BUT REMEMBER ... the third angle (which is what they ask for) is x - 30

So ... work it out from here?

Answer 5

a+b+c =180 by definition.
a= b+15 :given
c = b-30 : given

substitute in eq1:
(b+15) + b + (b-30) = 180
3b -15 = 180
3b = 195
b = 65
c = b-30 so c = 35
a = b+15 so a = 80
80+65+35 = 180 : check
35 is your answer