SOLUTION: In the triangle, measure of angle 1 + the measure of angle 2+ the measure of angle three equals 180�. If the measure of angle three equals two times the measure of angle one and th

Question 998399: In the triangle, measure of angle 1 + the measure of angle 2+ the measure of angle three equals 180�. If the measure of angle three equals two times the measure of angle one and the measure of angle one equals the measure of angle 2 find the measure of angle three in degrees
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let a = measure of angle 1
let b = measure of angle 2
let c = measure of angle 3

measure of angle 3 equals 2 times the measure of angle 1.

equation for that is c = 2 * a

measure of angle 1 equals measure of angle 2.

equation for that is a = b

sum of the angles is 180 degrees.

equation for that is a + b + c = 180

you have 3 equations that need to be solved simultaneously.

they are:

a + b + c = 180
c = 2 * a
a = b

subce a = b, let's replace b with a in the first equation to get:

a + a + c = 180

since c = 2 * a, let's replace x with 2 * a in the first equation to get:

a + a + 2 * a = 180

comtine like terms to get:

4 * a = 180

divide both sides of this equation by 4 to get:

a = 180 / 4 = 45 degrees.

since c is equal to 2 * a, then x must be equal to 90 degrees.

since a = b, then b must be equal to 45 degrees.

we get:

a = 45
b = 45
c = 90

the sum is 280 as it should be.

you are asked to find the measure of angle 3 in degrees.

since c = measure of angle 3, then angle 3 must be equal to 90 degrees.

these solutions satisfy all 3 equations.

a + b + c = 45 + 45 + 90 = 180 (good)
c = 2 * a = 2 * 45 = 90 (good)
a = b = 45 (good)

everything checks out - solution is good.

angle 3 is equal to 90 degrees.

RELATED QUESTIONS
If P is the measure of an angle, 180 - p is the measure of the supplemen of the angle. If (answered by funmath)

If P is the measure of an angle, 180-P is the measure of the supplement of the angle. If... (answered by stanbon)

If the measure of angle 2 is equal to the measure of angle 6 and angle 6 equals "X"... (answered by cleomenius)

in triangle efg the measure of angle f equals 3 times the measure of angle g and the... (answered by ReadingBoosters)

In triangle ABC, the measure of angle B is 2 more than three times the measure of angle... (answered by josgarithmetic)

if measure angle = 40 , find the measure of angle 8 (answered by tommyt3rd)

In a triangle, the measure of the first angle is twice the measure of the second angle.... (answered by Cromlix)

If triangle FGH, the measure of angle G is three times that of angle F. The measure of... (answered by fners)