Question

The second angle of a triangle is 4 times as large as the first angle. The third angle is 15 degrees less than the first. What is the measure for each angle

Answer 1

Let the measure of the first angle be \( x \) degrees. According to the problem, the second angle is 4 times the first angle, so it can be expressed as \( 4x \) degrees. The third angle is 15 degrees less than the first angle, which gives us \( x - 15 \) degrees.

The sum of the angles in a triangle is always 180 degrees. Therefore, we can set up the equation:

\[
x + 4x + (x - 15) = 180
\]

Combining like terms, we get:

\[
6x - 15 = 180
\]

Next, we will add 15 to both sides:

\[
6x = 195
\]

Dividing both sides by 6 gives us:

\[
x = 32.5
\]

Now we can find the measures of the three angles:

1. The first angle \( x \) is \( 32.5 \) degrees.
2. The second angle \( 4x \) is \( 4 \times 32.5 = 130 \) degrees.
3. The third angle \( x - 15 \) is \( 32.5 - 15 = 17.5 \) degrees.

Therefore, the measures of the angles in the triangle are:

- First angle: \( 32.5 \) degrees
- Second angle: \( 130 \) degrees
- Third angle: \( 17.5 \) degrees

Thus, the angles of the triangle are \( 32.5^\circ, 130^\circ, \) and \( 17.5^\circ \).