Can someome please help me with this?

Question

The first angle of a triangle measures 2 times the sum of the second and third angles. The second angle measures 30 degrees. Find the measures of the first angle

Answer 1

Let the three angles be X,Y Z with Y = 30

Since the sum is 180 we have:
X + 30 + Z = 180 ......(1)

and we are given
X = 2( 30 + Z).........(2)

Substituting we have (60 +2Z) + 30 +Z = 180

Solving for Z we get Z = 30 degree
accordingly X = 180 -30 - 30 =120

Ans: X= 120, Y =30 (given) Z= 30

Answer 2

The angles of a triangle sum to 180 degrees.
Let first angle = X , the second = Y and the third = Z
X + Y + Z = 180
You said X = 2(Y + Z) and Y = 30
substitute 30 for Y in the first two equations yielding
X + 30 + Z = 180 and X = 2(30 + Z) ==> simplify these to
X + Z = 150 and X = 60 + 2Z
substitute the value of X from X = 60 + 2Z into
X + Z = 150
(60 + 2Z) + Z = 150 ==> simplify to
3Z + 60 = 150 ==> simplify to
3Z = 90 ==> simplify to
Z = 30
substitute this back in the equation
X + Z = 150 ==>
X + 30 = 150 ==>
X = 120
so the angles are:
first = 120, second = 30 and third = 30

Answer 3

The second angle equals 30 degrees

The sum of the second and third angle equals

30 + 30 = 60

The first angle equals 60 degrees

30 + 30 + 60 = 120

120 the total degrees.

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The first angle equals 60 degrees

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Answer 4

a= first angle
b= second angle
c= third angle

a=2*(b+c) that is what the first problem sentence says
b=30 that is what the second sentence says

so,

a=2*(30+c)
a=60+2c
a-2c=60

we also know that a+b+c=180 (true for all triangles) so,

a+30+c=180
a+c=150

two equation two unknowns
1) a-2c=60
2) a+c=150

several ways to sove this, easiest probably substitution

a=150-c (from equation 2)

substituting in equation 1)
150-c-2c=60
-3c=-90
c=30

a=150-c
a=150-30
a=120

Answer 5

<1=2(<2+<3)
<1=2(30+<3)
<1=180-(<2+<3)
so equating
60+2<3=180-30-<3
3<3=90
<3=30*
<1=120*

Answer 6

120
120=2(30+30), equals 180

Answer 7

120 degrees
30+30=60
60*2=120