Question

together the measures of angle B angle C and angle D equal 180. The angles have the following measures: m angle b = 25 m angle c = 3x and m angle D = (3x +5) What are the measures of angle c and angle D

m angle c =
m angle D=

Answer 1

Given that the measures of angles B, C, and D add up to 180 degrees, we can set up the equation based on the information provided:

\[
m\angle B + m\angle C + m\angle D = 180
\]

Substituting the values of the angles into the equation:

\[
25 + 3x + (3x + 5) = 180
\]

Now combine like terms:

\[
25 + 3x + 3x + 5 = 180
\]

\[
25 + 5 + 6x = 180
\]

\[
30 + 6x = 180
\]

Next, subtract 30 from both sides:

\[
6x = 150
\]

Now divide by 6:

\[
x = 25
\]

Now that we have the value of \(x\), we can find the measures of angles C and D:

\[
m\angle C = 3x = 3(25) = 75
\]

\[
m\angle D = 3x + 5 = 3(25) + 5 = 75 + 5 = 80
\]

Thus, the measures of the angles are:

\[
m\angle C = 75^\circ
\]
\[
m\angle D = 80^\circ
\]