SOLUTION: Angle 1 = x + 7 Angle 2 = 2x-3 Angle ABC = x2 Find the value of x and the measure of angle 1

Algebra ->  Angles -> SOLUTION: Angle 1 = x + 7 Angle 2 = 2x-3 Angle ABC = x2 Find the value of x and the measure of angle 1       Log On


   

Question 901980: Angle 1 = x + 7
Angle 2 = 2x-3
Angle ABC = x2
Find the value of x and the measure of angle 1
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Angle 1 = x+%2B+7
Angle 2 = 2x-3
Angle ABC = x%5E2
by definition, the sum of all angles in a triangle is 180
so, angles 1%2B2%2BABC=180...plug in given values


%28x+%2B+7%29%2B%282x-3%29%2Bx%5E2=180
x+%2B+7%2B2x-3%2Bx%5E2=180
x%5E2%2B3x+%2B+4=180

x%5E2%2B3x+%2B+4-180=0

x%5E2%2B3x-176=0...solve for x
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-3+%2B-+sqrt%28+3%5E2-4%2A1%2A%28-176%29+%29%29%2F%282%2A1%29+

x+=+%28-3+%2B-+sqrt%28+9%2B704+%29%29%2F2+

x+=+%28-3+%2B-+sqrt%28+713+%29%29%2F2+

x+=+%28-3+%2B-+26.7+%29%2F2+
solution: we need only positive solution
x+=+%28-3+%2B+26.7+%29%2F2+

x+=+23.7%2F2+
x+=+11.85+
now find the measure of angle 1 :

Angle 1 = x+%2B+7

Angle 1 = 11.85+%2B+7
Angle 1 = 18.85


Angle 2 = 2x-3=2%2A11.85-3=23.7-3=20.7


Angle ABC = x%5E2=%2811.85%29%5E2=140.423
check their sum:
1%2B2%2BABC=180
18.85%2B20.7%2B140.423=180
179.9725=180 ...round to whole number
180=180