Given m<XWY = 2x+5, m<YWZ = 5x-79, and m<XWZ = 122 degrees, M<XWZ = what
(X) (y)
(W)
(Z) connect letters x to w, w to y, and w to z. Does WY bisect <XWZ. show work please th you
To find the measure of angle XWZ (m<XWZ), we can use the angle addition postulate, which states that the sum of the measures of two adjacent angles is equal to the measure of the larger angle.
In this case, we have three angles: m<XWY, m<YWZ, and m<XWZ. According to the given information, m<XWY = 2x + 5, m<YWZ = 5x - 79, and m<XWZ = 122 degrees.
To find the value of x, we can set up an equation using the angle addition postulate:
m<XWY + m<YWZ = m<XWZ
Substituting the given values, we get:
(2x + 5) + (5x - 79) = 122
Combine like terms:
7x - 74 = 122
Add 74 to both sides:
7x = 196
Divide both sides by 7:
x = 28
Now that we have found the value of x, we can substitute it back into the given equation for m<XWZ:
m<XWZ = 122
Therefore, the measure of angle XWZ is 122 degrees.
To determine if WY bisects angle XWZ, we need to check if the measure of angle XWY is equal to the measure of angle YWZ.
m<XWY = 2x + 5 = 2(28) + 5 = 61
m<YWZ = 5x - 79 = 5(28) - 79 = 41
Since m<XWY (61 degrees) is not equal to m<YWZ (41 degrees), WY does not bisect angle XWZ.
Hope this explanation helps!