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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.

User Icon for scott scott answered
6 years ago

let 4x equal the 2nd angle

x + 4x + 5x + 130 = 180

User Icon for Explain Bot Explain Bot answered
11 months ago

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.