Angle of a triangle?

Question

The second angle of a triangle is 15 degrees less than twice the first. The third angle is the sum of the other two angles. Find the measure of the angles.

I am stuck on this problem, could someone please help?

Answer 1

This is algebra. Remember that the three angles also sum to 180!

Let's call angles 1, 2, and 3... a, b, and c.

b = 2a - 15
c = a + b
a+ b + c = 180

Those are your three equations.
Now substitute b with 2a - 15
c = a + (2a - 15) = 3a -15
a + (2a -15) + c = 180

Now substitute c with 3a - 15
a + (2a -15) + (3a - 15) = 180
6a -30 = 180
6a = 210
a = 35

Now plug a = 35 into the other equations.
b = 2 (35) - 15
b = 55

c = a + b = 35 + 55 = 90

So there's your answer: 35, 55, 90

As a final check, do 35, 55, and 90 add up to 180 degrees?

Answer 2

First of all, u have to understand that the sum of two angles in a

triangle is always greater than the remaining angle. the sum of

two angles of a triangle is equal to the remaining when the

remaining angle is 90'. so according to your problem, the third

angle is 90'. if u want to estimathe the value of other two angles,

use algebraic method. let the first angle be 'x'

and second angle is 'y'. By the problem, y= 2x-15

since the third angle is 90, the sum of first and second angle is 90.

so, y+x=90, y= 90-x

so, 2x-15=90-x, 3x= 105, x= 35 and y= 90-x then 'y' becomes 55

degree.

Answer 3

a + b + c = 180

b = 2a - 15
c = a + b

c = a + 2a - 15
c = 3a - 15

a + (2a - 15) + (3a - 15) = 180
a + 2a - 15 + 3a - 15 = 180
6a - 30 = 180
6a = 210
a = 35

b = 2(35) - 15 = 70 - 15 = 55
c = 35 + 55 = 90

ANS : 35°, 55°, 90°

Answer 4

180 degrees...= the sum of the 2 other angles
75 degrees...=the 2nd angle
105 degrees...=the 1st angle

Answer 5

y=2x-15
z=x+y
X+y+z=180

substitute!
x+(2x-15)=x+(2x-15)+(180-[x+(2x-15)]-x)
Ta Da!P.s I'm taking trigonometry!