i need help with a question regarding angles the exterior angle theorem. it hase angles 140 8x+4 and 3x+4 but it wants me to find angle M<S
To find angle M<S using the exterior angle theorem, we need to know the measure of the two remote interior angles. The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
In this case, we have the exterior angle M<S, which we want to find, and two remote interior angles, represented by the expressions 8x+4 and 3x+4.
To find angle M<S, we need to find the values of x that correspond to the measures of the remote interior angles.
Let's equate the sum of the remote interior angles to the measure of the exterior angle:
8x+4 + 3x+4 = 140
Now, we can solve this equation for x:
11x + 8 = 140
11x = 140 - 8
11x = 132
x = 132/11
x = 12
Now that we have found the value of x, we can substitute it back into the expressions for the remote interior angles:
Angle S = 8x+4 = 8(12) + 4 = 100 degrees
Angle M = 3x+4 = 3(12) + 4 = 40 degrees
Therefore, the measure of angle M<S is 100 degrees.