9. In parellelogram MRST, m<M=3x-40 and m<S=7x-100. Find:
a. the value of x.
b.the measure of <R
Are angle M and S congruent? If so, 3x-40=7x-100.
yes they are
thanks
To find the value of x, we'll set the two given angle measures equal to each other and solve for x.
a.
Given: m<M = 3x - 40 and m<S = 7x - 100
Since opposite angles in a parallelogram are congruent, we can set up the equation:
3x - 40 = 7x - 100
Let's solve for x:
3x - 7x = -100 + 40
-4x = -60
Dividing both sides by -4:
x = (-60) / (-4) = 15
So, the value of x is 15.
b.
To find the measure of angle R, we can substitute the value of x back into one of the angle measures and solve for the measure of angle R.
m<M = 3x - 40
m<M = 3(15) - 40
m<M = 45 - 40
m<M = 5
Therefore, the measure of angle R is 5 degrees.