An illustration shows three rays extending from a common origin. The angle measures between them are labeled. What are the two unknown angle measures that form the 90° angle and we have X +4 and on the other side of that angle we have 3X +2 and the question is what are the two unknown angle measures that form the 90° angle and they have X +4 equals blank and 3X +2 equals blank what are the answers
To determine the two unknown angle measures that form the 90° angle, we need to set X + 4 equal to the complementary angle measure and 3X + 2 equal to the other angle measure.
Given that the sum of complementary angles is 90°, we can set up the following equation:
(X + 4) + (3X + 2) = 90
Simplifying the equation, we have:
4X + 6 = 90
Now, let's solve for X:
4X = 90 - 6
4X = 84
X = 84 / 4
X = 21
Now that we have found X, we can substitute it back into the original equations to find the values of the unknown angle measures:
Angle measure opposite to X + 4:
X + 4 = 21 + 4 = 25
Angle measure opposite to 3X + 2:
3X + 2 = 3(21) + 2 = 63 + 2 = 65
Therefore, the unknown angle measures that form the 90° angle are:
X + 4 = 25°
3X + 2 = 65°