Question

Together, the measures of ∠B
, ∠C
, and ∠D
equal 180°
. The angles have the following measures: m∠B=25°
, m∠C=(3x)°
, and m∠D=(3x+5)°
. What are the measures of ∠C
and ∠D
?(1 point)
m∠C=__°

m∠D=__°

Answer 1

We know that the sum of the measures of angles \( \angle B, \angle C, \) and \( \angle D \) is \( 180^\circ \). We are given the following measures:

- \( m\angle B = 25^\circ \)
- \( m\angle C = 3x \)
- \( m\angle D = 3x + 5 \)

We can set up the equation based on the sum of the angles:

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

Substituting in the values we have:

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

Combining like terms:

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

Now, we can solve for \( x \):

\[
6x = 180 - 30
\]
\[
6x = 150
\]
\[
x = 25
\]

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

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

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

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

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

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

Final answers:

- \( m\angle C = 75^\circ \)
- \( m\angle D = 80^\circ \)