Question

a triangle has angles described as follows: the measure of the first angle is four more than seven times a number, the measure of the second angle is four less than the first, and the measure of the third angle is twice as large as the first.what is the measure of each angle in degrees?

Answer 1

First angle: 46 degrees

Second angle: 42 degrees

Third angle: 92 degrees

Explanation:

Let's represent the unknown number as "x".

The measure of the first angle: 7x + 4

The measure of the second angle: (7x + 4) - 4 = 7x

The measure of the third angle: 2(7x + 4) = 14x + 8

Since the sum of the angles of a triangle is always 180 degrees, we can set up an equation:

(7x + 4) + 7x + (14x + 8) = 180

Simplifying the equation:

28x + 12 = 180

28x = 168

x = 6

Now, we can substitute the value of x back into the expressions for each angle:

First angle: 7x + 4 = 7(6) + 4 = 46 degrees

Second angle: 7x = 7(6) = 42 degrees

Third angle: 14x + 8 = 14(6) + 8 = 92 degrees

Therefore, the measure of each angle in the triangle is:

First angle: 46 degrees

Second angle: 42 degrees

Third angle: 92 degrees