Question

In the diagram below of triangle B, C, DBCD, EE is the midpoint of start overline, B, D, end overline

BD
and FF is the midpoint of start overline, C, D, end overline
CD
. If mangle, D, C, B, equals, 87, plus, 3, x∠DCB=87+3x, and mangle, D, F, E, equals, minus, 8, x, plus, 164∠DFE=−8x+164, what is the measure of angle, D, C, B∠DCB?

Answer 1

[AI-generated answer — Bot GPT 3.5]

Since EE is the midpoint of BD and FF is the midpoint of CD, we can use the midpoint formula to find the values of x:

Angle DCE = Angle BCF (because EE is the midpoint of BD and FF is the midpoint of CD, and opposite angles are congruent)
87 + 3x = -8x + 164
11x = 77
x = 7

Now that we have found the value of x, we can find the measure of angle DCB:

Angle DCB = 87 + 3(7)
Angle DCB = 87 + 21
Angle DCB = 108

Therefore, the measure of angle DCB is 108 degrees.