If m<1 =m<3=8x,m<2=2x-20,and m<4=x,find
the value of x.
To find the value of x, we need to compare the angles given and set up an equation based on their relationships.
Given:
m<1 = m<3 = 8x
m<2 = 2x - 20
m<4 = x
First, let's look at the angles:
m<1 and m<3 are both equal to 8x. This means that m<1 and m<3 are congruent angles.
m<2 is equal to 2x - 20.
m<4 is equal to x.
From this information, we can set up an equation based on the relationships between the angles:
m<1 + m<2 + m<3 + m<4 = 360° (since the sum of the angles in a quadrilateral is 360°)
Substituting the given values into the equation, we get:
8x + (2x - 20) + 8x + x = 360°
Combine like terms:
19x - 20 = 360°
Now, isolate x by moving -20 to the other side of the equation:
19x = 380°
Finally, solve for x by dividing both sides by 19:
x = 20°
Therefore, the value of x is 20°.