An illustration shows three rays extending from a common origin. The angle measures between them are labeled.
(X+4). (3x+2)
What are the two unknown angle measures that form the 90 degree angle
(X+4) degree = blank degree, (3x+2) degree= blank degree
To find the two unknown angle measures that form the 90 degree angle, we need to set up an equation.
The sum of the angle measures in a triangle is always 180 degrees. Since we have three angles, we can set up the equation:
(X+4) + (3x+2) + blank degree = 180 degrees
Since we are looking for the two unknown angle measures that form the 90 degree angle, we know that their sum must be 90 degrees. Therefore, we can set up a second equation:
(X+4) + (3x+2) = 90 degrees
Now we can solve these equations to find the values of X and the unknown angle measures.
Equation 1: (X+4) + (3x+2) + blank degree = 180 degrees
(X+4) + (3x+2) = 90 degrees
Combining these equations, we get:
(X+4) + (3x+2) + (X+4) + (3x+2) = 270 degrees
Simplifying, we have:
2X + 6x + 12 = 270 degrees
Combining like terms, we get:
8x + 12 = 270 degrees
Subtracting 12 from both sides, we have:
8x = 258 degrees
Dividing by 8, we find:
x = 32.25 degrees
Now we can plug this value of x back into the equation (X+4) + (3x+2) = 90 degrees to find the two unknown angle measures:
(X+4) + (3x+2) = 90 degrees
(X+4) + (3(32.25)+2) = 90 degrees
(X+4) + (96.75+2) = 90 degrees
(X+4) + 98.75 = 90 degrees
X + 102.75 = 90 degrees
X = -12.75 degrees
Therefore, the two unknown angle measures that form the 90 degree angle are:
(X+4) degree = -12.75 degrees
(3x+2) degree = 32.25 degrees.