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.
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