SOLUTION: The measure of one angle of a triangle is 20 degrees more than the measure of the second angle. The measure of the third angle is 30 degrees more than twice the sum of the measure

Algebra ->  Angles -> SOLUTION: The measure of one angle of a triangle is 20 degrees more than the measure of the second angle. The measure of the third angle is 30 degrees more than twice the sum of the measure      Log On


   

Question 164687: The measure of one angle of a triangle is 20 degrees more than the measure of the second angle. The measure of the third angle is 30 degrees more than twice the sum of the measures of the first two angles. Find the measure of each angle in the triangle.
Found 4 solutions by Fombitz, checkley77, KnightOwlTutor, Mathtut:
Answer by Fombitz(32388) About Me  (Show Source):
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Let's call the angles A,B, and C.
.
.
.
"one angle of a triangle is 20 degrees more than the measure of the second angle"
1.A=B%2B20
"The measure of the third angle is 30 degrees more than twice the sum of the measures of the first two angles."
2.C=30%2B2%2A%28A%2BB%29=30%2B2%2A%28B%2B20%2BB%29=30%2B2%2A%282B%2B20%29
Also, since it's a triangle you know that,
3.A%2BB%2BC=180
Use eq. 1 and 2 and substitute in eq.3,
3.A%2BB%2BC=180
%28B%2B20%29%2BB%2B%2830%2B2%2A%282B%2B20%29%29=180
B%2B20%2BB%2B30%2B4B%2B40=180
6B%2B90=180
6B=90
highlight%28B=15%29
from eq.1,
A=B%2B20
highlight%28A=35%29
from eq. 2,
C=30%2B2%2A%28A%2BB%29
C=30%2B2%2A%2835%2B15%29
C=30%2B2%2A50
highlight%28C=130%29

Answer by checkley77(12844) About Me  (Show Source):
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A=B+20
C=2(A+B)+30
A+B+C=180
(B+20)+B+2(A+B)+30=180
B+20+B+2(B+20+B)+30=180
B+20+B+2B+40+2B+30=180
6B=180-20-40-30
6B=90
B=90/6
B=15 DEGREES FOR THE MIDDLE ANGLE.
A=15+20=35 FOR THE FIRST ANGLE.
C=2(15+35)+30=2*50+30=100+30=130 FOR THE THIRD ANGLE.
15+35+130=180
180=180

Answer by KnightOwlTutor(293) About Me  (Show Source):
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<1=x
<2=x+20
<3=2(x+x+20)+30=4x+40+30=4x+70
<1+<2+<3=180
x+x+20+4x+70=180
Combine like terms
6x+90=180
Subtract 90 from both sides
6x=90
divide both sides by 6
x=15
Let's check
<1=15
<2=15+20=35
<3=2(35+15)+30=130
15+35+130=180



Answer by Mathtut(3670) About Me  (Show Source):
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Lets call the 1st angle A. Angle 2 which we will call B is 20 more than the 1st angle so A+20=B and the 3rd angle which we will call C is twice the sum of the the first 2 angles(A and B)plus 30 degrees so 2(A+B)+ 30=C....Lets solve for C in terms of A in this equation: 2A+2(A+20)=C simplifying C=4A+70. Now, we know that A+B+C=180. So lets plug in our values A+(A+20)+(4A+70)=180 solving for A we get A=15 Degrees since B=A+20 B=35 Degrees and C=4A+70 so C=130 degrees.