Question 998399
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.