The second angle of a triangle is 4 times as large as the first. The third angle is 130° more than the sum of the other two angles. Find the measure of the second angle.
let 4x equal the 2nd angle
x + 4x + 5x + 130 = 180
To find the measure of the second angle, we'll first set up an algebraic equation based on the given information.
Let's assume the measure of the first angle is x degrees.
According to the problem, the second angle is 4 times as large as the first angle. Therefore, the second angle would be 4x degrees.
The third angle is stated to be 130° more than the sum of the other two angles. The sum of the first and second angles is x + 4x = 5x degrees. So, the third angle would be 5x + 130 degrees.
The sum of all three angles in a triangle is always 180 degrees. Therefore, we can write the equation:
x + 4x + (5x + 130) = 180.
Now, let's solve this equation to find the value of x, which represents the measure of the first angle.
10x + 130 = 180 (combine like terms)
10x = 180 - 130 (subtract 130 from both sides)
10x = 50
x = 50/10 (divide both sides by 10)
x = 5
So, the measure of the first angle is 5 degrees.
Now, to find the measure of the second angle, substitute x = 5 into our equation for the second angle:
4x = 4 * 5 = 20.
Therefore, the measure of the second angle is 20 degrees.