Question

The measure of two angles of a triangle are in the ratio 3:4. If the third angle is 20 degrees less than the smaller of the other two angles, find the measure of the third angle.

Answer 1

In a triangle where two angles have a ratio of 3:4, and the third angle is 20 degrees less than the smaller of the two, the third angle measures 40 degrees.

Step-by-step explanation:

The student is asking about the measures of angles in a triangle, which is a Mathematics problem, specifically in geometry. The sum of angles in any triangle is always 180 degrees. To solve this problem, we can use algebraic methods and properties of triangles. Let's denote the measures of the two angles as 3x and 4x based on the given ratio 3:4. Because the third angle is 20 degrees less than the smaller angle (3x), we can denote it as 3x - 20.

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

1. 3x + 4x + 3x - 20 = 180

Solving this equation:

1. 10x - 20 = 180
2. 10x = 200
3. x = 20 degrees

Now we can determine the measure of the third angle:

1. 3x - 20 = 3(20) - 20
2. = 60 - 20
3. = 40 degrees

So, the measure of the third angle is 40 degrees.