An illustration shows three rays extending from a common origin. The angles between them are labeled. The first ray extends vertically upward from the vertex, the second ray is inclined upward from the vertex to the right, and the third ray extends horizontally to the right. The angle between the first and the third rays is marked with a right angle symbol. The angle between the first and the second rays is labeled as left parenthesis x plus 4 right parenthesis degrees. The angle between the second and the third rays is labeled as left parenthesis 3x plus 2 right parenthesis degrees.
What are the two unknown angle measures that form the 90° angle?
The angle between the first and the third rays is a right angle, which means it measures 90 degrees.
I need numbers.
Let's solve for the values of x in order to find the specific angle measures.
The angle between the first and second rays is labeled as (x + 4) degrees.
The angle between the second and third rays is labeled as (3x + 2) degrees.
The angle between the first and third rays is a right angle, which means it measures 90 degrees.
To find the value of x, we can set up the equation based on the given information:
(x + 4) + (3x + 2) = 90
Simplifying the equation:
4x + 6 = 90
Subtracting 6 from both sides:
4x = 84
Dividing both sides by 4:
x = 21
Now that we have found the value of x, we can substitute it back into the expressions for the angles to find their specific measures:
Angle between the first and second rays: (x + 4) = (21 + 4) = 25 degrees
Angle between the second and third rays: (3x + 2) = (3 * 21 + 2) = 65 degrees
So, the two unknown angle measures that form the 90° angle are 25 degrees and 65 degrees.