Question

The measure of the first angle in a triangle is x°, the second angle is the sum of 2 times the first angle and 3, the third angle is the sum of 3 times the first angle and 3. What is x?

Answer 1

The value of x, representing the first angle in the triangle, is found to be 29 degrees by setting up an equation based on the sum of the angles in a triangle being 180 degrees, and then solving for x.

Step-by-step explanation:

To find the value of x in the given triangle with angles defined in terms of x, we can use the fact that the sum of the angles in a triangle is 180 degrees. According to the problem, the first angle is x°, the second angle is 2x + 3°, and the third angle is 3x + 3°. We can write an equation that sets the sum of these angles equal to 180°:

x + (2x + 3) + (3x + 3) = 180

Combining like terms, we get:

6x + 6 = 180

Subtracting 6 from both sides:

6x = 174

Dividing both sides by 6:

x = 29

Therefore, the measure of the first angle is 29 degrees.