use diagram given: m<XWY = 2x+5, m<YWZ = 5x-79, and m<XWZ = 122 degrees. m<YWZ= what?
(x) (y)
(w) (z)
connect x to w, w to z, w to y
Does WY bisect ,XWZ? Please show work. Th u
2x+5 + 5x-79 + 122 = 180
7x = 180 + 79 = 259
X = 37
m<YWZ = 5x-79 = 5*37 - 79 = 106o
To determine the value of m<YWZ, we can use the given angles m<XWY and m<YWZ, as well as the fact that the sum of the angles in a triangle is 180 degrees.
Given:
m<XWY = 2x + 5
m<YWZ = 5x - 79
m<XWZ = 122 degrees
Since XWY and WYZ are angles that share side WY, we can set up the following equation to find the value of x:
m<XWY + m<YWZ + m<WYZ = 180
Substituting the given angle measures:
(2x + 5) + (5x - 79) + 122 = 180
Next, simplify the equation:
7x + 48 = 180
Subtract 48 from both sides:
7x = 132
Divide both sides by 7:
x = 18
Now that we have the value of x, we can substitute it into the equation for m<YWZ:
m<YWZ = 5x - 79
m<YWZ = 5(18) - 79
m<YWZ = 90 - 79
m<YWZ = 11 degrees
Therefore, the measure of m<YWZ is 11 degrees.
To determine if WY bisects <XWZ, we need to check if m<XWY + m<YWZ = m<XWZ. Let's substitute the values we know:
m<XWY + m<YWZ = (2x + 5) + (5x - 79) = 2x + 5 + 5x - 79 = 7x - 74
m<XWZ = 122 degrees
If WY bisects <XWZ, then m<XWY + m<YWZ = m<XWZ. Let's compare the values:
7x - 74 = 122
Solve for x:
7x = 196
x = 28
Since the equation does not hold true for any value of x, we can conclude that WY does not bisect <XWZ.