Question

Together, the measures of <B, <C, and <D equal 180. The angles have da following measures m<B = 25, m<C = (3x) and m<D = ( 3x + 5 ) wut r the measures of <C and <D?

m<C = ____

m<D = ____

Answer 1

We know that the measures of \(\angle B\), \(\angle C\), and \(\angle D\) add up to 180 degrees:

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

Given that \(m<B = 25\), \(m<C = 3x\), and \(m<D = 3x + 5\), we can substitute these values into the equation:

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

Now, let's simplify the left side:

\[
25 + 3x + 3x + 5 = 180
\]
\[
25 + 5 + 6x = 180
\]
\[
30 + 6x = 180
\]

Next, we isolate \(6x\):

\[
6x = 180 - 30
\]
\[
6x = 150
\]

Now, solve for \(x\):

\[
x = \frac{150}{6} = 25
\]

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

1. For \(\angle C\):

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

2. For \(\angle D\):

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

So the measures of \(\angle C\) and \(\angle D\) are:

\[
m<C = 75
\]
\[
m<D = 80
\]