Vw is bisected by xy and xz at x creating 3 angles if m< vxy= 6x-14 and m<yxz=2x+5 and m<wxz=2x-1 find the degree measures <vxy, <yxz, and <wxz
Draw a diagram. You see that the three named angles form a straight line, vw. Therefore, if you add them up, they must total 180°
6x-14 + 2x+5 + 2x-1 = 180
10x - 10 = 180
x = 19
Now use that value of x to evaluate the three named angles.
(6x-14) + (2x+5) + (2x-1)=0,when x=19,6x-14 well be 6*19 -14=100,when (2x+5) well be 2*19+5=43,when(2x-1) well be 2*19-1=37.the all three angles will be 100+43+37=180.
To find the degree measures of angles <vxy, <yxz, and <wxz, we need to substitute the given expressions for the angle measures into the equations.
Given:
m<vxy = 6x - 14
m<yxz = 2x + 5
m<wxz = 2x - 1
Since the sum of the three angles in a triangle is always 180 degrees, we can set up an equation using the given angle measures:
m<vxy + m<yxz + m<wxz = 180
Substituting the given expressions:
(6x - 14) + (2x + 5) + (2x - 1) = 180
Combining like terms:
6x + 2x + 2x - 14 + 5 - 1 = 180
10x - 10 = 180
Now, let's solve for x:
10x = 180 + 10
10x = 190
x = 190/10
x = 19
Now that we have the value of x, we can substitute it back into the given expressions to find the degree measures of the angles:
m<vxy = 6x - 14 = 6(19) - 14 = 114 - 14 = 100 degrees
m<yxz = 2x + 5 = 2(19) + 5 = 38 + 5 = 43 degrees
m<wxz = 2x - 1 = 2(19) - 1 = 38 - 1 = 37 degrees
Therefore, the degree measures of angles <vxy, <yxz, and <wxz are 100 degrees, 43 degrees, and 37 degrees, respectively.