Use the image to answer the question.An illustration shows three rays extending from a common origin. The angle measures between them are labeled.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?(1 point)(x+4)°=°, (3x+2)°=
The two unknown angle measures that form the 90° angle are:
(x+4)° = 90° and (3x+2)° = 90°
wrong
Apologies for the incorrect response. Let's solve for the two unknown angle measures that form the 90° angle.
From the image and given information, we have the following equations:
Angle between first and third rays: 90°
Angle between first and second rays: x + 4
Angle between second and third rays: 3x + 2
We know that the angle between the first and third rays is a right angle, which means it measures 90°. Therefore, we can set up the equation:
90° = x + 4 + 3x + 2
Simplifying the equation:
90° = 4x + 6
Subtracting 6 from both sides:
84° = 4x
Dividing both sides by 4:
21° = x
So, the value of x is 21°.
Now, we can substitute x = 21° into the equation for the angle between the second and third rays:
Angle between second and third rays = 3x + 2
Angle between second and third rays = 3(21°) + 2
Angle between second and third rays = 63° + 2
Angle between second and third rays = 65°
Therefore, the two unknown angle measures that form the 90° angle are:
(x + 4)° = (21° + 4)° = 25°
(3x + 2)° = (3(21°) + 2)° = 65°